My mother in law is in a nursing home she will not allow anyone of her children to take mom out for the day or lunch or holidays. my sister in law is not capable of taking care of herself let alone my mother in law. my brother in law signed my MIL out for thanksgiving and one of the other brothers picked her up my SIL threw a fit. so at Christmas he refused to allow anyone to take her out of the home except her. as a result my MIL fell getting out of the car and my SIL couldnt get her up. A stranger walking her dog stopped to help. this is one of many incidents we need her off the Medical POA Help!
Since Mom is in a nursing home, that means she needs a much higher level of care due to her Alzheimer's/dementia. What can happen is that when Mom is returned to her room and after the siblings have left, Mom might become upset, out of control, wanting to pack and move out, etc. That makes the job for the Staff all that more difficult trying to calm her down.
It could be that your Mom doesn't act up when your sister-in-law takes Mom out. As for falling out of the car, that could happen with anyone, anywhere.
I have seen it happen that when returned to Memory Care after a short trip, the person didn't recognize the place, grew scared and began to cry. It took a while to reacquaint her with her room, staff, other residents.
Plus, she may not remember once she returns, so the risk of her falling down, picking up a virus, etc. may not be worth the risks of taking her out. So, the POA's reasoning may actually have some good reasons behind it.
Make the best of the situation. Visit MIL often. Host small parties there for her. My sisters and I sometimes brought in a pretty table cloth, centerpiece, nice dishes, and Mom's favorite carry out food. We reserved a small community room. Special event for Mom without the hassle of leaving the premises. For holidays we reserved a larger room and set up a pot-luck buffet, with kids and grandkids attending.
There are other ways besides leaving the premises that allow for special meals and events.
Bloom where you are planted now.