How can I persuade my mother to attend a support group for chronically ill people?

I am the only caregiver for my elderly mother, who has numerous chronic conditions. I think that we both need to join a support group to help us understand that there are others out there who are suffering too. I'm convinced that the support of a group could help ease the feelings of self-pity and day-to-day depression my mother is experiencing. However, she refuses to go, and says a group would only make her feel worse. If nothing else, I think I need a group to help me deal with her illnesses and depression. Can you help?