No suggestions here, but I wish I had the courage to do what you are doing. My marriage has been so very unhappy for so long (17 years), and I didn't realize how miserable I was until I saw my husband making our child unhappy by treating her the way he treated me--with coldness, contempt, and little patience or quality time. Now that I've said I am through and want out, he's suddenly doing all those things he absolutely "couldn't" do before, like getting home from work at a reasonable hour, eating dinner at the table with us instead of sitting in front of the TV to watch his news programs or military history documentaries (nothing family friendly that we might all enjoy), helping with the dishes, even taking our daughter to the park to play on weekends instead of parking her in front of the TV and griping at her to be quiet. From being unable to get her dressed or do even the slightest tasks to take care of our daughter and himself, he is suddenly able to at least pick up a take-out pizza and help her get to dance class on time and in the proper attire. Funny how it wasn't worth his time or effort for the first 16 and a half years of our marriage, and how my complaining about his lack of time and attention and consideration was just me being bitchy. Yeesh.
With all of that as background, believe me, if any man at all showed up being nice to me, much less someone with whom I had happy memories, I would have a hard time not responding. So I wish you the best, I hope you can work through the bitterness with your children, and I guess I'd agree with everyone who says to take it slow when trying to integrate your new man into your children's lives. They do have to be your first priority, but that doesn't mean you aren't entitled to be happy. If you were on your fourth marriage, I'd say you're being selfish, but it sounds like you gave the marriage a good try.
Good luck to you and your family.