How do I convince my mother to move to be closer even though she's overwhelmed with the thought of moving all of her stuff?
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.
As a Senior Move Manager (see the National Association of Senior Move Managers--NASMM), I have this book in my library, and several others listed below this posting. Go to NASMM.ORG for more ideas on how to assist your parents. The Senior Move Managers who belong to this national association often offer informational resources on their websites. Sr. Move Mangers specialize in helping families make these tough decisions as well as arrange all the logistics. As for Missouri moves, please contact me! I'm in St. Louis.