This is a tricky situation, because you want to maintain respect and dignity, but you are genuinely concerned. Here are some ideas that may be helpful.
Seek out a senior companion - this is someone who is either paid to come and visit, or they volunteer to come and visit. This may be helpful, because they are her peer group, not family and are non-partial, except to improve the quality of her life.
Plan an acitivity twice a week that is out of the house. Tell her about, make it something she used to like doing or with people she like being with. Talk about it all week, everyday. Give her information about, if we are leaving on Tuesday at 11:30 am, you will need to be up at 9:30, shower, do you hair and eat breakfast, etc. Give her small steps to getting to the bigger events.
If she has a faith or religion, ask people to come and visit and talk with her.
Even if you are family and have her best interests in mind, she may be feeling controlled by you. If other people in her life start sharing the same information, she may be more open to it.
An adult day care center or a senior center activity may an options as well. The key is to get her re-engaged in life a little at a time on her own terms as much as possible.
One more thing to consider, is she experienceing paranoa and anxiety with the depression, she may need more psychiatric/ MD support to address these issues, because that can also create a refusal to leave her room, house or bed as well.