My brother lives and takes care of our Mom, many medical issues. We want our mom to go to nursing home. my brother will not do it himself, recently it took 3 of us to clean her up and put her in bed. my brother could not do it by himself. my brother is 60. I have power of attorney and so does my brother.
If your Mom is of sound mind tell her she will now need to hire Caregivers to come into help. If she says no, ask her what will she do.... let it be her suggestion as that makes it easier. If she continues to say she wants your brother to keep taking care of her, keep telling her that is no longer an option. He's too old to do that now.
I really believe that our parent(s) don't see us as aging ourselves with our own age declines and limitation, but that of a very young person with a ton of energy. My parents are that way :(
If mom is of sound mind you can't force her into care even with POA. However it's sounds like it's definitely time for her to be in care. Few people can provide this level of care at home and keep their sanity.
Search this site for loads of info on your question. There are some good articles here. I think you're going in the right direction. Good luck.