Aunt Maggie. So very sorry this has happened to you - and I have a feeling the advice you're getting on this thread isn't what you want to hear.
Like others have said, I imagine you're still in shock - a kind of post-traumatic shock. It also sounds as though your DP has fallen from the most enormous pedestal, in that you thought he was so different from other men who have treated you badly. I agree with those who say that since he knew you'd been hurt by cheating before, this was particularly cruel.
That said, your confusion might be rooted in a belief that only "bad" people have affairs. The truth is that people who are perfectly kind, sweet, empathetic etc. are having affairs - and are therefore capable of cruelty, as well as kindness. Good people have affairs.
I think you need more information Maggie. I'm not completely convinced you know everything there is to know. Why did the affair end, for example? What has the contact been between him and this woman since? Can he show you texts or E mails (showing you his passwords to any remote communication at the same time)? And what's the full story with the picture texts he received - I assume he didn't expect you to believe that a woman would send these unsolicited?
When I did my reading on infidelity, I noticed that several therapists commented that male infidelity within the first 10 years of a relationship was a bad portent. This is because it alludes to a man not being sure he can really commit to one person. If he's doing this before you are married and have had children - and at a time when you only have eachother to concentrate on, what will he be like when you have DCs competing for your attention, or money worries and the lack of "us time" in those infant years?
It is monumentally difficult to get past infidelity at any stage of life, but although you have invested 6 years, you have learned some truths now about this man before children and a long shared history, muddy the waters of whether to stay or go. In your shoes, I'd probably end the relationship, because of all the warning signs I've mentioned above. However, if you do stay with him, don't even entertain getting married and having children until he has got to the root cause of his behaviour and established whether this abusive act (an affair is abusive) is symptomatic of his personality.
The biggest clues to whether he is really contrite are in his actions. Does he want to understand why he did this, as much if not more than you? Or does he hope that now his conscience is clear, it can be swept under the carpet, without ever learning anything about how it was possible to be this cruel to someone he was meant to love? Words are easy - actions are difficult.
Maggie, the other thing I wanted to say is that this is not your fault. The fact that others have cheated says far more about the men you have loved, than it says about you. Infidelity is a choice. Often people will come up with huge justifications for it, but it is always a choice people take rather than being honest with their partner about wanting someone else, as well as, or instead of their partner.
Far more often than you think, it isn't because there was anything wrong with the primary relationship, apart from a bit of boredom. Some people take up the opportunity to be unfaithful simply because they can - it isn't because it's a fault with you or the relationship. It's because of supreme selfishness and a sense of entitlement on the part of the betrayer. These are the character faults your DP should accept and work on, either with you or without you. And it is not your responsibility to ensure he does.