Honestly I don't think that this is okay. I mean if he wanted to spend some quality time with his kids, he shouldn't take them on a trip with a woman who has feelings for him but whose not dating him to a destination that isn't exactly known for its kid friendly attractions. It just doesn't seem to add up. If he really wanted to spend time with his kids but also go on a trip, he should just take them to a fancy amusement park (Disney Land, Disney World, Universal Studios, etc.) or something and leave his ex out of it. They're his children so he should be able to take care of them without the help of his ex. And if he does happen to need help, he should ask the person he's dating (you). I mean is it really that difficult to think up that one? I don't know, the whole situation your boyfriend is currently in just seems really fishy to me.
So yeah, I don't think that this is a good idea. I mean I'm not an adult who has had experience with boyfriends with children, but this just logically doesn't make sense. That's why I suggest that you confront him about this. Just tell him that it doesn't make sense for him to have to go somewhere with his ex if all he wants to do is spend quality time with his children. Also note that his ex seems to have feelings for him and it makes you uncomfortable. If he says that you're overreacting, then it's pretty likely that he has something to hide. I'm not saying that this is always the case, but it's pretty likely that he's got something he's not telling you. If that happens, you should break up with him because everyone deserves someone who treats them well and isn't trying to just sneak around behind their back. Yeah you could argue that he's great to you and that he's a really good guy or you could be harsh and say that you don't think that there's going to be anyone out there like him who'll love you, but I honestly don't think that it's worth being in a relationship like that. I think that you are better off single than being with a guy who is sneaking around. But if your boyfriend understands you and agrees to change his plans, then that's good news. If he is trying to justify himself or understands but isn't willing to change plans, then be especially critical to his reasons and be wary. This is kinda on the fence and you'll have to make a decision about this yourself based on your guts.
Anyway, best of luck to you!