EDIT: Oh wait, I was in the right thread, I just forgot I had another page to look though. Heh.
That doesn't seem like the best situation for you. You definitely need to talk to her about this situation. Even if she was just being playful with this fella, it's still off and it's still wrong for her to do so. Doubly so if you didn't know this guy was in your girl's life. I mean... if he was a close friend you knew about beforehand, then maybe I can understand her language. But, I'm not getting that based on your posts.
Talk to her after the trip is over. You've said your relationship's been rocky and she's been blowing you off. It's sort of the tipping point now. You need to get her to talk to you about your relationship, the possibility of emotional cheating, and if she continues to blow it off, you need to break it off, because she's clearly no longer caring about your feelings.
I understand it can be difficult to move on from a long relationship, if you feel you've invested "too much time into it"... that's why my previous relationship of 7 years lasted as long as it did, when it really only should have lasted 4. But, you shouldn't put yourself in a position wherein you're miserable just because you've put time into it. If you do that, it's not going to magically get better--in fact, in situations like that, spite and resentment tends to make things a lot worse.
Uh, the silent treatment? How old is this guy? That's not a mature way to deal with anything. You say "how will he be able to deal with anything in a marriage if he can't deal with petty things"? The answer is, he won't, simple as that.
He's pushing you off and that's not fair. You're only encouraging it, though. How so, you may ask? By being with him, and forgiving him for his silent treatment bullshit consistently by letting him talk to you 'on his terms', and never on your own. You want to marry a jackass that refuses to talk to you for days on end? That's not a healthy relationship at all. He needs to grow up, but you aren't really giving him a reason to. It seems he's outright antagonizing you for whatever reason, why do you keep dealing with that?
He doesn't love you, clearly. Stop subjecting yourself to an antagonistic asshole that (appears to) enjoy making you heart-broken. Everyone deserves better than that.
Why not, just... not... go? Why put her and yourself at risk of being around this supposedly very violent man?
Actually.
Hold up.
If he's very violent, how does he have custody of the kids (or are allowed to see them at all)? How can he drop them off at her place without supervision? How does she not have a restraining order if he did all these things? Typically violent, terrible people like what the ex-husband sounds like would need these things in order for her to be able to attempt a divorce. She'd at least need some kind of protection against him, if he's done all that. In most domestic abuse relationships like that, the husband wouldn't just be like "oh, a divorce? okay". Even if it's going messily as you said legally... people like that usually do more than just legal stuff to the partner.
Something feels a little off. Not to discredit her claims (I know that sounds incredibly heartless)... but do the kids have anything to say about the about how their father acts? If he was really that violent, wouldn't they not want to go see their father?