Waiting for the shoes to drop. Any suggestions?

Your mother has Stage 4 Alzheimer's Disease that has been documented by a doctor and you are her legal POA.
You are responsible for handling her financial matters and making sure she has adequate housing and care. You're saying that she refuses any kind of outside help. It's not for her to refuse or accept because it's not her decision to make anymore. She is incompetent and it is documented. You make her decisions now. You can bring in homecare help. You can put her into care also. She doesn't get a say because you're the one in charge and the one who is responsible for her.
Let her rant and rave until kingdom come about not being able to drive. If there's no access to a car she isn't going to be driving anywhere.
You are right about doctors and many other health care professionals not being willing to tell an elderly patient a hard 'NO' on some things like driving. They don't want to deal with an angry, irate, demented senior throwing a fit in their office and disturbing everyone. That's understandable.
Depending on what your mother's finances look like, you may also be able to put her into respite care in a nursing home or memory care when you have to travel for work.
Talk to your state's Ombudsman's office. They will be able to help you find out what services are available for mother.

When the shoe dropped for us it was mom calling 911 for everything: sheriff's deputies came out at all hours for reports of mom's missing dog (not missing), being locked out of her house (she was calling from her living room), a noise outside, people walking up her driveway and looking in her windows (no people). As for her car we disabled it (took out battery) because she was unsafe driver. She lived near a school and could very easily back up into a child walking by. We didn't want that on our/her conscience. Mom didn't cook but stored medicine, paperwork, and old bird nests in the oven. She turned on the oven once and could've burned down the house. As you say you're getting by and you will continue to get by until something terrible happens. Don't let that happen on your watch. Mom lives with me now since about a year. The next step will be Memory Care.

Read your POA. Does it say immediate or you need one or two doctors to deem her incompetent. If the latter, get those letters saying Mom is no longer competent to make informed decisions. Now you POA is in effect. Its no more what Mom wants, itscwhat she needs. She needs to be in an AL if she has the money to do it. If not, Medicaid in a nice LTC facility. You cannot leave her home alone. My Mom left a pot of water to boil. I had to throw out her favorite pan because she forgot she left the pot on the stove.

Your Mom at this point has lost her short-term memory and the ability to reason. You now are the adult and her the child. She needs to be somewhere safe so you can continue doing your job without worrying about her.

The shoe has ALREADY DROPPED all the way down.
Yes, if she is stage four and diagnosed as such you need to REMOVE the car. Take the car to a trusted friend's for storage. Embrace your duty to tell Mom it is no longer safe to drive. Take her and her license to the DMV and get her a senior ID to replace the license.
No, you cannot now leave your mom with a diagnosis of stage IV dementia alone. You are responsible.
It is time for you as POA (your Mom's funds pay for this) to see an elder law attorney about your duties as POA. Discuss your options. Once a senior is demented it is no time to easily get out of the duties you ACCEPTED as POA, and from all you say I think you are not aware, even of what your duties are.
Please see an Elder Law Attorney ASAP.
If you cannot do these duties your Mom will become a ward of the state. You will need the help of an attorney to resign and notify authorities that you Mom needs the state to step in as conservators. At that time your Mom's assets will be used by the state for her care. You will have nothing to say about placement, when, where, or her finances.
Wishing you good luck. Get that appointment today. Tell them you need to pay hourly fee to learn your duties under the POA document now that your Mom has been diagnosed with stage IV dementia.

My dad was leaving my mom for 90 minutes to go to the grocery store and that wasn't OK. Think about what your mom might do (or not know what to do) in the case of a fire, or if she turned on the stove and walked away? There are myriad scenarios where she could be in real danger.

You need a Plan B for when you're gone whether she likes it or not.

I don't know about the legalities, but traveling for 10 days at a time without having someone at least look in on her daily will likely be difficult if not impossible as she becomes more debilitated. I agree with Grandma1954 that she needs a caregiver or to be in respite care for when you're away for extended periods. It's very tough, I know.

Frankly the fact that she has been diagnosed with dementia and you are her POA leaving her alone for 10 days is not a good idea. Any number of things could happen and you as POA might be held responsible. What if there was a fire? Would she know what to do? Would she know to call 911 and leave the building? What if she fell? Could she call 911? In both cases unless you live in an area with "enhanced 911" if she can not give an address it will take longer for EMS to get to her.
She no longer has the capacity to decide what is best for her/safe for her. The reason you are POA is because she can not make those decisions any longer.
Would you leave a 4, 5, 10 year old alone for 10 days?
The choice is having a caregiver come in while you are gone or placing her in Respite while you are away. (If your sister will not stay or bring her to her house.)
Disable the car. Better yet remove it from the property so she can not see it. Eventually "out of sight out of mind" will prevail.