On happy, it's only an assumption that he is happy. If your H gets those chemicals generated in his brain and body that come from a new lust... then he gets to feel "happy"... but it's temporary. If he is actually capable of leaving you, moving in with someone else, and "finding his happiness" with no further thought about you or his past... then there is something wrong with him at a core level and I'm not sure why anyone would want to be with someone like that...
No, more likely he gets happy, then the OW does something and it triggers the "do I really want this" thought... or other life gets in the way... he isn't "happy" in the way you want to believe... or in a way that he'd WANT you to believe and says he is... he'll tell everyone he is happy ALL THE TIME (which is a lie as humans are biologically incapable of that), and try to project that, so that he can prove that he made a good and right decision... even if it's to convince himself...
The first things he offered as the "reasons" were probably just him stretching the truth. That those "things" really weren't that important. He was just giving you bait so you'd leave him alone and work on your "problems".
He asked for space, you gave him space... and you thought that by giving him the space he had been asking for, that he would change his mind and start closing that gap...? Yes, that's the game of pursuit and distance, but just because it is generally in play, doesn't mean that they will... they may need to be away much longer than we expect... which is the problem... expectations... that if we give them what they ask for, they will change their mind and direction...
Ponder this... exactly WHAT does space mean?
The truth is, it means absolutely nothing...
It is simply a word... a phrase we use to say, "I need quite time to think about things"... or "I'm saying it to distract you as I continue to leave"... or "I hurt all over, emotionally, and just need to drop out for a while"...
Unfortunately, the word is intended to be abstract enough so that the person saying it does not have to confront what they are currently thinking.
The harsh reality that you need to face is... what if...?
What if... he never comes back...?
Because the reality probably is... that's what you fear the most, right now... and it could happen...
so...
what are you going to do about it? If he never comes back... how are you going to tackle your life and make it the best you can, for yourself... for your kids...?