What are some things an out of town sibling can do to support the in town sibling?

I am the caregiver for my 89 yo mother, and have 4 out of town siblings. Dad passed a year ago, Mom lives in a 55+ independent community. She is very social, still drives in familiar surroundings and pretty independent. However, she is lonely for Dad after a 67 yr loving marriage, and covid has cramped her style. She worries all the time about useless things and then can't get to sleep. Then calls me, any time day or night. Her polymyalgia slows her down when it flairs up. I take her to all her doctors appointments and visit her 1-3 times a week. These visits usually involve a little chore. Last week it was rearrange the furniture! Or bring all the Christmas decor from the garage to the apartment, put up the tree etc. Then take it all down a while later. Crawl behind the desk to retrieve something that fell down there, flip the mattress, blah blah blah.....
Who knows what it will be next! I truly enjoy time spent with Mom and these favors usually include having a lunch or dinner with her. But it's unpredictable and endless! She thinks of something and seems to need it immediately. When my siblings ask what they can do to help....
Oh, wait, they don't.

When I ask for help from my siblings it's hard to specify what they can do. I have concluded the most valuable thing they could give me is some time. So I have asked them to each call her once a week, at their convenience, and spend no less than 30 minutes on the phone with her. They each chose their day to call so it would fit their schedule. And the call should no be simply "how you doing Mom? Gotta go now". It should be a real conversation. Talk about a book you've read, have a discussion about To Vax or Not To Vax, tell Mom what her great-grandchildren are up to. Mom is up on current events, intelligent, open-minded and articulate and can hold her own on any topic. She can facetime and would love to see her great grandchildren. And if she talks to someone else every day she is not as likely to call me several times a day.
I ALWAYS answer when she calls. And she calls a couple times a day. One call can easily take an hour. I don't know if she could be calling to say hi or to tell me she's in pain, or has fallen. I never get a break from my phone and would love it if I could go out with friends and leave my phone home. Or stay home and watch tv and not carry my phone into the bathroom or kitchen everytime.
Sadly, it works for a week or two, then falls apart and I just hear "I haven't heard from your brothers/sisters in weeks".
As an out-of-towner, more contact with the loved one would help the caregiver a lot.
Mom's situation will decline, I know. She will need a lot more care. I went thru my Dad's years of Alzheimers without much help from siblings and I don't have the strength, emotionally or physically to care for Mom without help when the time comes.
So, out-of-town siblings, give your loved one a call. Even if they don't know who you are, strike up a conversation, read a story, have a Show Tune sing-along, ask about favorite dishes, vacations, pets from their past. Older people love to tell about times they mis-behaved and got in trouble (or got away with it!) Be creative. You might just enjoy spending time with your parent when the focus isn't on health/money/living arrangements etc.

I am the out of town sibling my brother is in town and we have actually found a way to complement each other well. Now much of that is because we work together well, talk and or text almost every day, though when one needs a break the other can take over to provide it. Now we do a lot of management through virtual devices which allow us to “manage” her day to day needs from wherever we are (me from home 5hrs away and brother the pilot from…) still she needs hands on at least every few days and the small emergencies seem never ending, that’s basically my brothers burden since his home base at least is there. But here’s how I am able to take a lot off his plate.

I do most of the scheduling and communicating with doctors because it can all either be done on line or via the phone. I do the waiting on hold or waiting for a call back, messaging through their messaging systems. I also order all the medications, do all the forms etc and order supplies that are then delivered. COVID got us to set up on line grocery shopping as well so I do that with her and then my brother or someone picks it up (they load the bags in the car) saves him so much time! He of course has to pick stuff up, new meds, meds that didn’t come in time…take her to appointments, though I do try to schedule those I can when I’m going to be there, all the on the ground stuff. Often during doctor appointments he will have me on speaker phone and of course the doctors know me and are used to how we balance things so that works. I do take my turns getting her up and taking pills, blood sugar etc, checking in several times a day and then same at the end of her day (walking her through getting the station she wants on the tv, lol) all via her Echo Show’s and the camera we have over her med area but for the most part he is hands on and I’m everything else. It makes the whole package so much easier when you can share the load and have someone to discuss with. Sometimes it’s just helpful to have someone to vent to or bounce ideas off of that is also intimately involved.

I live 200 Miles away but I talk to my 90 yo folks 2-3 times per day everyday. Just to say hi and I love you. Listen to their stories no matter how often they tell them. I go there about 1-2 times per month and bring them to my house for a few days. I am trying to get them interested in senior living but they refuse to leave their home of 65 years. My brother takes them out to breakfast or dinner. He helps with things as he can but works full time.
We also do video chats with them and the grandbaby who is here where I live. Fortunately they don't need physical care yet but groceries and socialization is important. It's a real sacrifice to drive three hours each way but I don't want to have any guilt or regret after they pass.
I like someone's idea about them getting mail. I will start sending them packages like grand baby art or photos. I also like the answer about doing the bills and such but be transparent w your siblings so they don't suspect you are pilfering money. Make copies of transactions to show them.
If you live so far you need to fly in, perhaps get a delta skymile card And rack up flying Miles..to use for the visit .
Best wishes to you! We are all in this together!

This is always hard, because what you really need is hands on, for the day to day cleaning, shopping, repairs, doctors, meals. You can ask for weekly shopping through Amazon Pantry, local supermarket delivery, etc which will save you trips.
You can ask for financial help for a cleaning lady. More frequent phone calls to check in, maybe even daily will maybe foster a closer relationship with your sister so that your Mom will WANT to go see her. The week away will be a wonderful break for you - so pretend you're going away so Mom will find it harder to resist going to your sisters. My advice is to take whatever you can get, because as time goes on - so will your mothers needs.

If sis will take mom for a week here and there, JUMP ON THAT! If mom can't really be alone, make up some kind of a little white lie about you NEEDING her to go since you are going somewhere or getting the wood floors refinished or whatever. Take the choice away from her since the break is for YOU not her. Ugh. Annoying.

Or can sis come to your place and you actually do leave? If mom won't agree to leave, then....

$ is always a nice help too. Unless mom can afford to hire a cleaning person, a helper of some sort, then sis could help with that.

What are you doing that can be done long distance? Banking, paying bills? These can be done on line and might take some of the stress off you.
Having her take mom for a time would be a great thing but if mom has a problem with not being at home it might be easier for your sister to come for a visit and you get out. You can book a get away or even swap houses with your sister for a few days. Or if you are caring for mom but have your own home, own life just going home and not having to deal with things for 3 or 4 days is a big help.
Or simple as it sounds the simple act of making dinner every night when you are a caregiver is exhausting. Order meals, have groceries or a meal delivered. Just make sure they know that a delivery is coming. (hate to have a bag of groceries sitting by the front door all day.
Hiring a cleaning service 1 time a month or even as a 1 time deal would be appreciated. (maybe)
And hiring a caregiver 1 day a week or more would help you out a lot. You might have to ease into it with mom but she will get used to it. (have them start while you are still there all day and just do little things then you "have to run to the store for an hour" or go for a walk. It will get mom used to someone new.
This is something that she may have to get used to anyway as she declines and you need more help. You will not be able to leave her alone and there will have to be someone there 24/7

Have your sister handle the mail and pay all the bills. If you have a trusting relationship, have her take over all the financial management functions and help you by contributing to a fund to pay for alternate care to go on a vacation, even if you don’t go far. Try to plan her visits far in advance on a regular schedule so you will know when you can plan a vacation, hit the road, leave town or visit friends without being encumbered by any responsibility for your mother.

In addition to what other folks mentioned above (coordinating bills, etc.): information gathering. If someone needs to be called, something needs to be researched (insurance, benefits, "does she qualify for...?", anything that would require digging through tedious documents online or calling somewhere where you're going to need to sit on hold), etc, that's also something that can be done long-distance. Depending on the question/issue, the out of towner might need PoA or to be given HIPAA waiver or something, but sometimes for information-gathering, those aren't needed.

Also, if the person is internet/technically savvy and an organizer...let them organize anything that needs organized! Let them draw up schedules, organize documents/files on Dropbox or Google docs, etc. If there's multiple people trying to help, then maybe an online calendar of who's coming to do what when would be helpful. If everyone's always wondering what happened at that doc appointment, maybe an up to date document where doc visit summaries are posted would be helpful. These sorts of things can be managed from everywhere - just make sure the organizer is sent all the info, and let them organize it/put it where people can find it.

As far as bill paying, my mother in law's money was at Merrill, Lynch. When I handled her money, Merrill would send a monthly account transaction copy to all the concerned relatives, etc. Some will let people check online. When my mother started failing and was isolated, I called her every day. Just small talk, but it meant the world to her. Also, as you do it more often, it becomes easier just to chat. It doesn't seem so much like "Making Conversation". Some online food sites have nice meals you can send for an occasional treat, or baked goods, or whatever they like. It is nice to get a surprise in the mail. I personally found it more helpful to have help several whole days a week. I could plan around those days. It was also easier to take my mother in law out (she needed a chair) grocery shopping, etc., with another person. Aggie really enjoyed any outing.

Find a high school or college student that likes old people to visit and do odd chores several hours a couple times a week. They can help with odd jobs, visit, take them outside, watch tv with them and have snacks. Often, a young person really cheers up us old folks. Even a young mother who meets the liking grandparent qualification might like a job a couple days a week during school hours to do such things. Just socializing and helping out. Maybe light housekeeping. Heck, Mom might like to see her kids occasionally. A young woman with a baby. Aggie adored babies. In fact, when she went to assisted living, all the ladies LOVED babies. Check with your church, local schools, etc. for recommendations.
Also, ANYTIME another relative can come, even not planned, is a good time. You don't have to be there all the time; they can learn the routine. You are around for backup, which they worry about.
Also, tell them how MUCH placement will cost, and they will have to share the expense and/or difficulty of talking Mom into it. You will not continue doing everything. They might decide to cough up more money for help at home after that.

I'm the out-of-town sister myself. When I go to see my mother, I make sure to schedule and take care of as many doctor's visits, etc., for my mother as I can, so my sis doesn't have to do that. Before the pandemic, we'd go shopping, etc. I order some of her clothing online, and try to take care of any difficult communications that need to happen, as my sis doesn't do well with any of that. Mother is in assisted living, so we have a great deal of help. However, it really is important for you to be very specific with your sister about what would help. Develop a "schedule" for that help to occur, then follow through with it. If it is financially possible for your sister, I agree that contributing toward some outside help so you can get a break would be really great. It sounds as though your mother has always been a difficult person. That is not going to change, and will probably become worse as she ages. Gird yourselves for that, and proceed.