First off, don't ask anymore if she's okay; it isn't really working out. You don't like hearing her say, "I don't want you to think that I want to get back together", do you?
A) It's okay to accept the invite, but don't always accept. Have other plans some of the time.
B) Keep focused on yourself. A lot of your post was about how she appeared to be down, or is now facing reality, or whatever she is doing. Move forward with YOUR life and let her live hers however she's going to. When you see her, put your best foot forward, but don't fawn over her or give her inordinate amounts of attention. Keep focused on your children and just be happy and yourself.
C) You pretty much have to just let this play out. Don't hold your breath that she'll be back knocking at the door, but you can improve your chances by being an attractive choice.
You cannot be lonely if you like the person you're alone with. Dr. Wayne Dyer
