Act like the husband you want to be. Make each and every interaction with her build her desire for you.
Apologize if you haven't. Have you considered asking for hope through a weekly date with her or something?
Side thought - I don't see why the kids would move if she has any hope...but kids shouldn't be moved if they don't need to. She's in a small rental, not your home. If she left, she suffers, not the kids...
