You will learn a lot when you read DR. Also, if you get a chance read "Not Just Friends" By (I think) Shirley Glass.... and then take a look at "Getting Back Together," "For Women Only" and then basically pick up all affair/relationship/marriage books you can and skim though them.
But DR, will really give you good advice on your sitch. Make a "cheat sheet" which you hide in a safe spot (where husband won't find!) and read, re-read and try to commit to memory useful information you learn there. Doing that REALLY helped me!!!
By the way, I think there's a difference between chasing and occassional invitations for events. Because he wants to see his kids (and you want to keep that relationship strong) I think it's okay to invite him over to see what he's missing (as long as he's interested in coming over and all contact is very positive... you want him creating good memories of you and the kids). I always made sure I looked STUNNING (and sexy!) when husband came over (either to visit, pick up kids, etc..), and I was always cordial, friendly (but not overly so)... although I would be a little flirty sometimes!!!, joking, happy... I made sure I asked him lots of friendly questions (nothing personal or about OW), about work, how he was doing, feeling, health, family,etc... Let him talk about himself and just listen and be supportive. As books on men point out, men want respect. A little ego building is nice too!
Another thing. My husband loves his kids too and I knew he missed them terribly. I also know my husband tends to dislike being "left out" of family events. So during the divorce I made sure I did a lot of fun things with the kids. I took them to festivals, museums, outings, etc... and I'd take lots of photos, and put them up in the house so my husband could see all the fun things he was missing by not being with his family.
Another thing, even though I'm pretty clean about my house, I made sure whenever he was over it was VERY "homey." Candles, flowers, positive vibes, a place that anyone would want to live in. Of course, now that he's back I try to keep it the same way!!! He's going out of town tomorrow, but I'll make sure the house is clean and nice before he leaves and I'll put flowers in the vases and that way he'll take with him good mental snapshops of his home and family when he's not here.
So.... my suggestion is stop worrying about OW and focus on yourself and your kids. Use this "break" from your husband to rework yourself into an even more amazing person!