Do not invite him at all. His choice was to be away from you and you need to respect that. Go with the kids, have fun, take pictures and post them on FB or messenger so your family can see the boys and you.
Red, I know it hurts but he don't just left and got some time out, he left because he is in A, and this A is with your X-Friend. I know you want him to go, I know you think that it could be nice and he can see that you make a great family together.
But this is not the way. You do that and the clock goes back big time. Go and have fun as much as you can, your H is out of the picture because he chose to be. So let him be.
It will take some time for him to change his mind (if he does). You need to do your stuff now. Go places with the boys. Just make sure to just work as adults around the schedule. And this has nothing to do about you and him. It's about the kids.
This hard work your having been putting on is not for you to just throw away. It's for you to treasure. If you believe in the process then be patient.
Wonka wrote this to Raine sometime ago: Do what works, if it is not resonate with you as the right thing, then it is probably what you need to be doing.
It spoke volumes to me because we keep saying that our actions may seen contra-productive, but the truth is that the more we go back trying to be nice, the more we hurt our cause.
Right now, it is time to do your things by yourself. As the time go by and he may come around, then you will think about it.
Let him have time for his A, the more time he has for it, more are the chances they will implode.
Have faith, be mysterious, be fun, be confident, let him go.
Then when you are far from danger, cry inside the closet. And don't eat the ice-cream. It's no worth it. You need to be gorgeous, girl power and girl rules. Eat lettuce, not ice-cream.