Come on ..... surely we have all been friends with people throughout our lives who, it then transpires, has a horrible child(ren), husband, friends or dog. You cannot turn a switch on and like someone if all your instincts are screaming that you don't.
Obviously though, most of us would be polite in company of said horrible person (child/friend/husband/dog .... yeah, I do appreciate a dog isn't a person) when our paths crossed but realistically, we would almost certainly try to arrange to see our friend when contact with the people we don't like can be minimised. And yes ..... that can be bloody tricky sometimes - especially with children - because they are usually around a lot more than a husband for example - and often calls for a great deal of diplomacy.
To be fair to the OP, it does seem as if - so far - this friend hasn't been excluded from get togethers or playdates. And it's fair enough to say that the boy's behaviour could be exacerbated by the fact he doesn't have another boy to play with and acts up because he is bored. However, all of you who think the OP should go on holiday with him regardless are nuts (or true saints perhaps ?).
If the friend is a very close one, and the 4 of you usually do everything together, then she probably would feel hurt at being left out ..... unless you feel she is the sort of person who acknowledges that her son is challenging, and who'd readily admit that a trip away would also be a strain for her, if she felt she had to concentrate 200% on him to ensure he wasn't upsetting anyone else (though it does sound as if she's pretty laid back about it).
So ..... I agree in so much that unless you can talk frankly with her (and only you can sum the risk of doing that up) then it's probably best to go away without any children at all.
However, I don't think you should feel guilty for disliking her son per se. Yes, he's a child - and of course, I am sure you make allowances for his age in reagrds to his behaviour - any reasonable adult would, but, if, having done that, you still don't like him - you don't like him, simple as that. Kids are people too - just smaller versions - and we can't automatically fall in love with everyone we meet.
I hope you get something sorted out - both with the holiday, and, going forward, with this friend and her son as I'm sure it can't be easy maintaing a friendship when you have such strong feelings about her child, even when they're justifiable (and that includes your frustration at her "different" parenting style).