I took care of my Mom in her home for about 3 yrs. She also appointed me as her POA. Now she is in assisted living. Such as washing her clothes, getting her pull-ups, rushing up there in case of an emergency. My 3 sisters say I am. The only thing they do is visit her every now & then.
To address your question, someone does need to do certain tasks. Will AL do the laundry? You can mail order pull ups (HDIS) addressed to Mom in care of the AL. I still visited my Mom every day (unless I knew someone else would be there). Like your Mom, mine had memory loss. If you are living close, the visits need not be long, I often incorporated it on my way to lunch with a friend or whatever. My sibs NEVER did get that someone had to bring in the body wash; mend the hems of her clothes and replace buttons, replace sleepwear and look out for her in general! You do need to check regularly with the AL on her nutrition, weight, doctor's visits, etc. And like the other posters noted, try a little outing. A visit to a nearby park or ice cream shoppe can be a boost for someone in an AL.
I take her favorite drinks, toiletries, clothes, etc. and see if there is anything else she needs. However, there are many in the ALF that do not have visitors. Some of them have family who live far away and never visit. The ALF must notify them when the resident needs things and they either pay extra or mail the items.
The ALF notified me that an appointment had been made for my LO to see the podiatrist and the day and time. They transported her. So, even though I"m the POA, the only thing I really have to do is be there in case of emergency and ensure payment is made each month to the ALF.
You may take out the POA that appoints you and read it carefully. It should state all the things you could or should be doing, even though your LO is in AL.
An online friend of mine has her mother in an NH. Her mom always wears socks. This friend decided to take off her socks and was shocked how her mom's bottom feet had these bad blisters and sores. She tried to get NH to get her mom to see a podiatrist. They dragged their feet on it. She tried to get her brother who has POA to get NH to do something, he dragged his feet on it. With you having POA, you have the power to insist that something be done if your mom's care is not up to par.
Here's my suggestions: if mom can go out and do her shopping and the AL has a system for them to do this, I'd push her to do this to see if she can get her own pull-up's. If she can't manage, then maybe set a morning once a week that you bring things in for her and put them up in her room. On the laundry, are they providing that and including it in the fee? If so, then let them do it. Make sure that everything is always labeled with her name and her initials in a couple of places.
Emergencies? like what & who is calling you? If it's mom, she just needs to slowly adjust that others are there to help her. If it's the AL, what are they calling about? This would be of more concern as it could be that mom isn't quite at the level of care that the AL is designed for and she may need a higher level of care. It's tough when then are coming form being at home to really evaluate whether they are best in IL, AL or NH. If it's the AL that's calling you and it's pretty frequent don't be surprised if they want to schedule a care plan meeting to go over mom's situation and what may be an issue for their level of care abilities.