I'm so sorry. I wish there was something I could do. It is all about H -- he has made it that way. He is obviously in a great deal of pain over his situation. And he feels unloved and disrespected (nevermind your efforts to prove otherwise). But he has become abrasive and mean-spirited in dealing with it (or not dealing with it). There's no excuse for that, and he knows that down deep.
This storming out the door is typical. But at the same time his threat to be gone all weekend is unwise and puts himself in a position where he might do something outright foolish. He is tempting fate, whether that's his conscious intent or not.
His inner turmoil is not something anyone else can resolve for him -- he has to do it. Your H is going to have to work through this himself. And childish displays of anger and frustration are not going to help matters. Nor seeking escape through external distractions. He has got to do this himself. And given his current attitude, I am afraid that Fallgirl is right, your H is not going to respond positively to demands that he or the both of you seek therapy. Not at this time.
You can continue to offer love and support for H while he goes through this. But otherwise back off from him -- and tend to your own needs and that of the boys. He wants to rebel against and blame something or someone for his frustrations, so don't let yourself become his scapegoat.
I think James Dobson's Tough Love approach is in order. If you've never read that book, I highly recommend it. (He basically suggests that one lead off early with what we know as LRT.) If you were close by I'd love to personally hand you my own copy.
Irish, please take care of yourself for now. Hug those boys. And give your H his space -- love him enough to do that, even though that might be the toughest thing you've ever done. Lovingly detach. Let him know that you still love him, but don't stand in his way. If he does something utterly foolish, then he is shooting himself in the foot. It will be his loss.
I will continue to pray for all of you that your H will eventually come to his senses.