Yeah this makes sense to me.Let her live with you for a while since you lived with her for a while. Seems fair.
When my mother was alive I'd do anything for her, and my girlfriend did a lot too. Idk what we'd ever have been able to do something like buy her a house, just cus we don't make enough, but I think I'd push for more manageable options. Buying a house doesn't seem like the first step towards fixing a bad situation, seems like a large step.
There are plenty of things you can do to help out that feel more beneficial to you and her. Like letting her stay with you.