My mother just recently had surgery for a broken femur is still thinking that she can live independently. How can I convince her otherwise?

Gosh. 97 and living independently up to now - impressive, no?

If I were you, I don't think I would try to convince her of anything. No real need. If she hangs on to the goal of getting home ("once you're strong enough we'll figure it out") that is a good incentive for her to give her rehab her best shot, and she's more likely to co-operate. And then either she will manage a serious miracle and become fit to return home, or at least she will gain maximum benefit from rehab and recover some quality of life.

So don't rob her of motivation if you can help it. Forcing her to acknowledge out loud that she can't live alone is too close to rubbing her nose in it.

Is she in rehab?
If she is, you have a wonderful opportunity to take professional advise about her living situation.

Btw, she's going to fall no matter where she lives.

It's only been a week, but she has shown signs of not being able to live without help. She has had minor falls, so this last one was probably inevitable and she is not able to clean up the kitchen, bath, etc. She is 97. She is also very hard of hearing.

Ditto what BB asked. What's the problem?

Is she currently in rehab? What do the therapists at rehab think about her returning to live alone?

Why are you convinced that she shouldn't be living independently?