What a mess... 
Unfortunately, it's not just the possibility of her losing her close relationship with her older cousin/cousin's children - but she's also running the risk of losing her relationship(s) with the rest of the extended family. I can't see her cousin's parents, siblings, grandparents taking too kindly to the level of betrayal. I know I wouldn't. Does she understand that she's likely to end up the source of family gossip (the nasty kind) for potentially the rest of everyone's lives? The "oh that's X, she broke up her cousin Y's marriage - caused no level of harm to poor Y's two little ones... don't trust her with your boyfriend/husband, dear, just in case she tries it on with him, too!" sort of whispers and sideways looks if she's brave enough to attend a family event? When this affair comes to light - and sadly, it probably will, irrespective of whether you tell the cheating husband, the betrayed cousin, or simply encourage your SD to end it - that is what is going to happen.
My aunt had an affair - not with her cousin's husband, no, but with her husband's best friend. It ended their marriage, and she married/had children with the best friend. That was a good 30... 35 years ago - and her own side of the family, so not even her first husband's side, still bring it up every time there's a family wedding/funeral/get-together. Even her own mother didn't take too kindly to what my aunt chose to do... but my aunt, at least, was a lot older than 19, and far less impressionable as a result (she had 3 young children, though, two of whom took their father's side and still refuse to have contact with their mother - her younger children, by her second marriage, have grown up hearing the aged aunts and their grandmother mutter darkly about their parents affair, and have distanced themselves from the wider family as a direct result... and no; I don't blame them).
Whilst your stepdaughter made the choice to get involved with the much older husband of her cousin... ought she to be the one who is blamed for the fact that it's happened at all? I don't think so. I think if she's never had a boyfriend before, if she has low self-esteem, if she admires her cousin so much - she was ripe for the picking. Perhaps she wants to be just like her cousin? Perhaps she actually doesn't like her cousin as much as you think, and is jealous of her - so is subconsciously trying to push her out of her own family, so that she can take her place? Maybe, deep down, she wants the security, the family set-up, the house, the children (albeit her cousin's by this... "man"), and is frightened of finding it by herself (ie, with someone who isn't her cousin's husband!).
But the 36 year old married father is entirely at fault here. He has preyed on a vulnerable young woman (at that age, they all do stupid things because they can't seem to work out the consequences of their own choices/actions, I'm afraid), groomed her into an affair (and you really do need to try to find out how old she was when this actually started - because I, like others, suspect she was a lot younger than 18!), flattered her, built her up to think that he's going to break her cousin's family apart for her... and now she's perhaps a little more assertive, he's getting the "when will you leave [cousin]?! When are we going to tell her about us?!" sort of questions, he's panicking. He's not going to leave cousin and their children, his nice cosy life where he has his cake and eats it too... He's probably never had any actual intentions of breaking his family up. Not for your stepdaughter, not for the girls he's most likely cheated on cousin with before your stepdaughter, and not for those who will replace your stepdaughter...
Tell him you know. Warn him off. And prepare yourself, and your stepdaughter, for the consequences of her choice to betray her cousin.
- this is such a mess... and for what? 