Mewho, it sounds to me as well, that something is off. What is her relationship with your parents? Does she have reason to be jealous of your parents? Is she feeling afraid or anxious? Does she feel unwelcome in any way? How old is she?
She might know that she is “off” in some way and is having anxiety about it. She might be scared to be alone in her home for Shabbos when she can’t pick up a phone or turn on the TV, etc. It is pretty obvious that she needs to be loved, needed and wanted. After all she is alone.
There comes a time in everyone’s life when our lives turn around and WE start to take care of our parents. It is called the sandwich generation. We need to do this with humor, generosity and with respect. It is NOT always easy. Yes, it can be very difficult at times, but we have to give back to our parents what they gave to us. As she cannot go to her other child as you pointed out, she has no choice but to go to your husband, her son. It is his and your obligation to care for her and by understanding this maybe you can do it in a pleasant and respectful way, and not find it so much of a burden. Let her know that she is more than welcome in your home. Let her have a sense of safety and security. Let her feel that she is NOT a burden to you but a welcome family member. Let her know how she can help so she feels needed. Include her in what is going on, ask her to test the kids on their spelling words. Set the rules by saying, “thats OK Mom, I have that under control” or “that’s ok Mom, Chanie knows the rules about candy before dinner”.
When she does leave she will be leaving knowing that she will be welcomed back with open arms and that she does not have anything to worry about. If she doesn’t want to leave, then know that she needs you more than you thought she did and work on yourself to accept that.