I hate to say this, but the only time a man walks in at 6am and 8am is when he's coming home from another woman's house. Don't no clubs stay open that long, and I'm sure his buddies don't stay up playing dominoes that long.
I am not one for telling anyone to walk out on a marriage, but as a Christian, you do have the right to leave if he is cheating on you.
But, personally, especially since children are involved, I would try to work on it before walking out.
It's difficult though if the other party isn't fessing up or acknowledging their wrong.
He has to admit his wrongdoing first before you even begin trying to fix things.
Have you asked him if he's cheating?