Sometimes the best way to get a parent to move is to say "Let's move what you need right away, close up the house, and come back in a month or two to get everything else."
People think they need so much more than they actually do. If you can get her to move first, she will realize later on that she doesn't need all her "stuff."
You also need to be more firm. Tell her what you said in your question -- that caring for her is important, but you need to consider your job and your family. You must establish boundaries.