The twin thing does complicate the issue somewhat, though. It shouldn't, of course, but "shouldn't" never stopped people from being . . . well, people. Especially if the twin pair have spouses who -- for whatever reason -- can't stand each other. (Because I'm fairly certain that however much the LW dislikes the sister-in-law, the sister-in-law reciprocates in spades.)

In that case, I can imagine at least one way the vacation thing could have happened: "Hey, Twin! If just you and I go and take your kids, then we can all relax and have a nice vacation without spending the whole time wondering when your wife and my wife are going to snap and start going after each other with the barbecue forks."