The one thing you seem definite about in your op is that there is no future for you and your current boyfriend.
I would say, first and foremost, end things with him.
(I say this as my H left me 18 months ago, affair, all the same script, coming and going, doesn't know what he wants! I thought the only way to move on was to find a new man. I did. And it helped me immensely in a lot of ways through some very difficult times. But his 'little annoying habbits' soon became big annoying habits. And as much as I enjoyed his company, I knew there was no long term future in it.
I took the brave step to end it with him and be totally alone. It was hard. But the best thing I've ever done. It's given me the time and space to focus on myself and come to some conclusions about H and I, what I want, and the future.)
As for your H, I would definitely be saying to him that he doesn't just get to pick and choose if/when he comes back. This is no longer about what he wants. He wanted to leave. He had his choice. He chose her.
I would want to see him living alone with no contact with her for a start. Can he actually show committment to getting you back? Can he live alone and work on himself? Can he prove to you that he has changed enough to be trusted again?
He can't just have the 2 of you waiting and jump between both beds houses as and when it suits him! As much as you don't need a man to make your life complete, he shouldn't need to be with someone.
What he does need is a kick up the arse and some time alone to reflect on all of this!
Is his loyalty with her or you?
If you reject him will he stay with her?
If I were you I'd want to know that if he is genuinely that unhappy with her, he'll be leaving her anyway? No matter what you decide.
Otherwise what happens next time you two have a bad patch - he runs off back to her?!
If he's just trying to weigh up which is the better option I'd tell him to stay put with her!!
There may well be a future for you both. But he needs to understand and accept that it is a long road ahead.
And I think some time alone for you would help you to clarify all of this in your own head. The new boyfriend doesn't sound like he makes you happy. (Doesn't matter that the dc like him!) Your husband doesn't sound like he deserves you.
Your future could well be with neither of them. You never know what's just around the corner.