The thing is, remorse would help to get over a 'mistake' but he took a few days to think about it, then did it again, even worse he had a year to think about it - then did it again! Not getting there is much regret there. That's even if what he says is true, you already know he's a liar, as has kept a lie for a year. Ever so lonely, but not so lonely that he couldn't conceive another child after it.
Just because some get through infidelity, doesn't mean you have try to. So, if he is being transparent, he will have shown you that her number and all ways of possible communication to her have been expunged from his phone? He will have promised she is now an ex-'friend' and will never see her again? Has he offered all that up?
I think you will find there has been more recent shenanigans going on, up to the time you challenged him, so during 2nd DC's appearance probably.
For me, it would be a hard no, based on putting you and your unborn DC at health risks, because I bet he didn't use condoms, not if it was spontaneous and a whim as he's trying to make out - he's minimising, they were clearly both up for it, and most likely did fancy each other. I'm a nurse though, so putting my health at risk is the more unforgiving side of me. I don't do jealousy, because it's the cheating person who is lacking and not good enough at the end of the day.
However, I would think, the only way to ever hope to get it in their skull what they've done, is by kicking them out for a time, then having counselling whilst not living together, and maybe, a few months down the line, going on occasional dates and see if there is still a connection worth fighting for.
While he was ' being lonely', was he leaving you to all childcare matters, or was he truly an interactive, fully involved father? If he was, he should put in effort to coparent, you should at the least have a trial separation and see how it goes.