It depends on how you see it...
Personally, I think the particular strings attached rules you gave them were stupid and just asking for trouble. Either pay the extra 2 bucks so that's not a problem or don't give them the password to begin with. Do you seriously notify them every time of your vacation dates? Did it really not occur to you that this could happen? Teens probably know more about resetting passwords than most parents do.
You could get the parents involved, but y'know, if I was your sibling, I couldn't see bringing myself to care about the whole deal or any of the drama from it. I'm DOUBTING this is a money issue. I would bet that like to my parents, they don't consider Netflix a necessity. It's not. This is (because you haven't got parental authority over the kids) a gift. Punishing the teen's siblings is just going to look really petty to everyone concerned. "Change it and not tell her" is not an adult choice, and just asking for drama...so yeah, don't pick that one.
I'd cut the strings, pay for the extra screen, and call that their Christmas gift. That's...24 dollars a year, for presumably 4 gifts. Bargain. And probably something they'll use more than whatever you get them, because if this is really such a big deal to you, I'm doubting that you buy much for gifts anyway.