My mom is a hundred in December I wanted to get mom a cake and to be with her family but my sister has said that we are not doing anything as mom wouldn't like it. Do you think I should do what my sister says or invite her family? Mom is in a care home.
https://www.agingcare.com/questions/my-mom-suffers-from-alzheimers-she-is-turning-90-and-im-not-sure-how-to-celebrate-her-birthday-448249.htm?orderby=recent
Try to understand why your sister thinks it is a bad idea, and work around it!
You have quite a while to come up with a better plan. What about asking family members to contribute cards and photographs, and making a nice, clear montage that you and your sister can share with her on the day?
Cake is always good, though :)