Sister refuses to place Mom in a home. Mom is 100 yo and lives by herself. What do we do?

We've had the family meetings. A sister in law has done a spread sheet a couple of years ago. Nothing ever comes of it. Thank you for the responses. Mom will either fall then be placed or God will take her in her sleep.

So, no one can force a POA / Executor to do anything?

The younger siblings are mentioning, have a sense of dementia / extra forgetting of details in the Executor...(perhaps it's stress...) which is why I am wanting someone, who is not this Sister to be appointed as executor/ POA.

Yes, powerless, helpless and the two younger siblings are angry and exhausted. I suggested to the two couples who live near her to move in with her. Mom has a large home with 5 bedrooms and 2 bathrooms. I was shot down like a skeet shooter, are most of my ideas. I can't even upgrade her toilet to comfort height or place safety rails in the bathroom. This is a very unsafe situation.

Most of the things you are concerned about were be very much the same if your mother was in an assisted living or nursing home situation. You don't mention any actual unsafe situations, only things that many people are dealing with due to Covid. In my father's assisted living they have had only a limited period where the communal dining room was open and being used. Most of the time since mid-February meals have been delivered to resident's rooms and they eat alone. If a resident leaves the facility for any reason, including medical appointments, they must quarantine (not leave the room, special precautions by staff, etc) for two full weeks. Now, it is a more supervised environment so your mom wouldn't be able to flood the place but it actually seems that aside from that incident not much would be improved by trying to wrestle your mother into a nursing home. Your sister needs to be more specific as to what "she can't do this anymore" actually means and give specific ideas on what help she needs. Then you can work to figure out how to provide her that help but I don't think that your can litigate your way to a different situation.

Tell your sister in a non threatening manner first that you think mom needs a social worker to help out. Hopefully she'll be agreeable, but even if not, your next step is to contact APS and report a vulnerable adult.

Litigation will not work, will cause more dissention and will be enormously costly. If your Sister is the POA or Guardian for her Mom, as well as caring for her in the home, there would be no way to convince a court she cannot do this; a huge fight could result in the state taking guardianship, which would lead to no one having any say about Mom's placement or her finances.
I think, until your sister is willing to put Mom in care there is little that you can do. She knows the choices. Continue in caring or stop.The family is killing themselves in enabling this situation by being there for her.
A poster recently told us that being a caregiver can kill you, and told us of her own illness and its costs. This isn't unusual.
I am so very very sorry. You simply cannot change the choices of other people. Constantly fighting her pushes her into her corner. Next time she tells you "I cannot do this anymore" tell her that when she is ready to consider change you will all call the family together to hash out what the options are. You must feel utterly helpless, but trust me, sinking 1,000s of dollars and escalating this situation is unlikely to help.