I had a similar emergency my senior year of undergrad while preparing for grad school. You've gotten good advice so far. Talk to whoever you feel comfortable talking to about it, which will hopefully include your advisor and/or your program director. Take advantage of campus counseling services. Remember that no one is going to judge you for taking incompletes or if you take some time off to be with your mom. On the other hand, don't let anyone pressure you into taking time off or incompletes if you don't want to. Some people need work to help them stay sane.
Take care of yourself however is best for you. This is really, really important. Spend time with friends. Be sure they know what you need from them- comfort, laughter, a shoulder to cry on, whatever.
Do spend time with your mom. Don't let her illness become the focus of your relationship or the time you spend together, but whatever you do, don't let yourself regret not spending enough time with her. Have fun together.
Remember: You're not alone. You have faculty in your program who will understand and help you figure out what to do. You have friends who will do whatever they can to help. Do what works for you.
Your mom is lucky to have you nearby. Good luck to both of you.