Long post, but I actually got through it.

Haha. Can you make some more specific questions? From what I just read, it looks like you're doing fine, and just need to give it some more time.
Suggest some one-on-one opportunities, dates, outings, whatever you want to call them, and make sure you take care of the kids before hand, by arranging for a babysitter. If there's a problem here, it's probably just that she's concerned for her kids, and it would probably be best to not involve the kids as much as you can avoid, so that she doesn't see an attachment from them as a problem just yet. You don't want the kids attached before she's made up er mind of whether she's going to spend time with you or not.