I agree about the "gut" feeling but also be aware that some times this requires counterintuitive action.
I think that given your expressed desire to fight for her. You should provide for her. Be a safe, considerate friend, live your life so you are happy and a desirable person. I would not ask her out right now, you know she's under pressure. I would back off for a week or so and give her the space she asked for.
I would watch out for mind-reading. More than anything, you have messed with her head and she needs space to figure her feelings out. You don't know what she feels. If my H wanted to come back at the juncture you're at, I would feel so messed with. I may not want him back but I would be miserable at the prospect of having to be responsible for saying no to him and my family being together...you see? It is a bit of a trap. She finally accepted your choice and now it is back on her. I don't know if she feels empowered by this in any way. But, depending on her personality, she may consciously or not, want to mess with you right back. Really, you don't know what she is going through.
I would want my H to SHOW me he was ready to be with me and be a family. I suppose that would mean he sets up therapy for us, he agrees to Retrovaille (google it), he makes demonstrated sacrifices to his social calendar to be with the kids and eventually us as a family.
You are attempting to undo damage you've done. I think it takes time and actions she can see are real. Anything you say you are going to do, make sure you do it (so don't overstate what you can do).
I still think you need to gain her respect too. I think you need to make sure you are fulfilled in your own life and create an environment that any woman would want to be in. She had given up on the vision of her family being together so, in time maybe being together as a family will be the strongest pull...it would be for me.
