Hi Elizabeth,
My family and I really enjoy bringing extended family on our trips to Walt Disney World. It is so much fun for everyone when there are more people around to share in the magic. One of the great things about Disney Vacation Club is the ability to book villas which allow everyone to come together and stay in one place.
Disney's Beach Club Villas is a great resort for a family vacation. I love the relaxed theme, and is is wonderful to be able to walk to Epcot in so little time!
My mother has accompanied us on a stay at a Disney Vacation Club resort, where she stayed on the sleeper sofa. She said that she found the sleeper sofa to be comfortable; however, I should say that she does not have back and knee problems, so I am not sure if that will impact your mother's comfort. My mother also said that since she had been walking around theme parks with us, including our young daughter, all day that she was so tired that she feel almost immediately asleep when we returned to the villa and slept soundly through the night!
I hope that these thoughts are helpful for you, Elizabeth. Have a great time planning your vacation, and please do not hesitate to ask if you have any further questions.