Is the birthday party already arranged? Were invites already sent out and are kids planning to come? If so, then perhaps your husband can have the kids after the party (then maybe YOU can go out and party!!!!).
If not, I like the idea of a pizza party at a public place with the kids, friends and your husband (a great reminder of family things he's missing! ;-)
If nothing has been planned yet, then let your husband have the kids. Since you have them 24/7 you probably need a break.My gosh!!!! Go out and GAL!!! have fun!!!!!
Since he currently doesn't spend a great deal of time with the kids, it's probably best to let him have them when it's convenient for him. Do whatever necessary to keep that relationship together. Your boys need it for their well-being. I understand it's maddening for you and you have a lot of anger towards him and there's a part of you that probably wants to hurt him. But you don't want to sever that relationship. I've seen too many dads pull away from the kids and eventually that relationship diminishes. And believe me, OW is probably thrilled you want to keep the kids all the time. Oftentimes it's kids who end up making waves in new relationships and marriages. Many girlfriends are jealous of non-bio kids and would prefer as little time with them as possible. They want the boyfriend all to themselves. I've heard that's a common problem...
There is no arriving, ever. It is all a continual becoming.