I think if it's too awful for you to tell us, then you'll never be able to cope with it. I think that your dp should have told you and as for making you feel your family is not as good as his because you come from a 'broken home'! Well - that is appalling! I'm beginning to think his family is a bit too close and would be healthier if a relationship had broken....
When you say to eighteenthirteen1, 'something like that' at the suggestion his parents are cousins [which would not be illegal], I think you mean they are either brother and sister or parent and child.
If they could not tell you and expect you to have children in the same lineage, I think it is very selfish of them., especially since someone else knows who told you.
By the way, we fall in love with people similar to us, I was taught in my psychology degree, right down to matching ear lobes in many cases. Apparently, twins, not even identical [or they would need to be gay] who are separated as babies, if they meet after puberty, can't wait to get into bed together - to quote my Tutor. Apparently there is plenty of research on this but it's not my field, I just remember being taught it. Were the two concerned brought up separately, thus didn't grow up together and then met as adults? That could explain it.
But as for getting married. No. He must have known this would floor you. He should know you well enough now. But it was dishonest not to tell you. That is what puts me off most.