Good: You already know not to appear desperate. What I think is going on is that she's falling for you and that's kind of rattling her. When we start having feeling for someone new, it triggers all those old unresolved feelings and hurts from our past relationship. Kind of like "A once scalded dog thinks twice."
The fastest way I know of to torpedo a relationship is to proclaim your undying love before the other person is ready to hear that. (Been there; done that; got the t-shirt.)
The reality is that she's got some scars and she'll just have to work through them.
Things are going your way. What you need to do now is back off and just be the low-pressure guy in her life. She occasionally needs a night away from the kids. Ask her to do fun things and be careful not to project that you expect anything from her. If you play it cool, I think you'll like where this is going.
Order this book.
Amazon.com: Love Tactics: How to Win the One You Want: Thomas W. McKnight, Robert H. Phillips: Books It has some of the best suggestions on how not to shoot a blossoming relationship in the foot that I've ever seen. At this stage, you don't need to impress her; just be irresistibly likable. The book will tell you how to do that.