I'm new to this all myself, but my gut instinct upon reading your posts here and in another thread: You are not ready for this yet, AND YOU DON'T HAVE TO BE IF YOU'RE NOT.
Maybe this is harsh, I don't know. This is one of the reasons when my husband and I married we both made it clear that if we were going to meet someone else we should talk about it rather than cheat. We've been through ups and downs in our years together, and if I'd met my new boyfriend even a year ago, I wouldn't have moved on this, because it wasn't a great time for us for a lot of reasons. I can't imagine opening up my marriage if we weren't okay with US. Sure there are situations where that's how it starts, but every healthy poly relationship I've seen starts from a place of respect, and the fact is you're hurting a great deal, feeling horribly pressured and like this is your only option, which means your feelings aren't being respected as much as they could be.
Respect involves you not having to dig to find out what's going on. It sounds like he's being open with you only when he gets caught; this cannot work if that's his attitude. I want to be encouraging, I really do, but seriously, there's cheating and there's polyamory. If you feel like he's cheating every time he's with her, that's not okay. If you feel like you have to interrogate him to get to the truth, that's not okay.
If you decide to open your marriage for him, that involves your feelings mattering as much as his and his new lover's do. Just because he takes another lover doesn't mean he can stop working on your marriage. That's not polyamory. If you're feeling jealous, he needs to give you more than lip service and genuinely work to make things okay with your relationship. You deserve better than that and should be honest. Pretending to be okay will only hurt you more and allow him to think that he can continue treating you with such disrespect.
Good luck to you. I really wish you the best.