Honey, if the worst thing he saw in those IMs was that you didn't think his gift was sincere, you deserve a GOLD STAR!
I know it feels like a step backwards, but hello, he expects you to trust him and ends up at OW's house?! Of course it will upset him to see that he's hurting you. (It's good that he cares about that.)
Don't trust any of what he says...just let it slide off your back with this attitude: If he's truthful, fine. If he's not, fine. This is what detaching is...finding happiness in yourself, not attached to ANYTHING he does. Finding the positives just become bonuses when you're not depending on them for survival.
I think you're a lot like me in that you feel you have to apologize, even when you're not ultimately in the wrong because you just don't like to have misunderstanding or negative feelings between you. I'm still guilty of it. But I am trying (and succeeding every once in awhile) to let responsibility lie where it should...I worry that by being too kind and accepting I am enabling his bad/neglectful/apathetic behavior. You don't have to be confrontational about it, just not so apologetic...reality is that his actions ARE hurting you deeply. If he's looking for reassurance that you're trusting him, how does that help either of you?