I would say there's a lot more going on here than just the obvious. It's easy to say that these aren't your children, you are just dating their mother and they aren't living with you, so you have no rights to them - but - to put her authoritative foot down over something like this? ...after 2 years? ...hmm, I'd begin wondering if you have a future with this person at all.
Yeah that's what I was thinking. If after two years together she is putting her foot down about you wanting to take her child to an event that he would enjoy and she won't let him go because he may be out a little late??? Me thinks something else is going on. That just does not make any sense. Two years is a long time to be around a woman and her children and if you have spent a lot of time with her kids then I don't get what the problem is.
She obviously doesn't feel like you make wise choices or would be a good father figure; otherwise, she'd be open and communicative ...not throwing what amounts to a 'hissy-fit' over this.
Unless we are missing something her reaction seems really immature.