Sometimes it sucks having choices, doesn't it?
Seriously, though, I think that's part of the problem. When it's YOUR kid, you obviously can't just walk away--even though, let's be honest, there are always days when you feel like it. The kids' dad and I used to say on a regular basis (before there was war and terrorists training there) that we wished we could put a stamp on ours and mail them to Afghanistan.
I don't think anyone is a horrible person for not wanting to establish a household with somebody else's problem kids. Or even non-problem kids, if you don't like the dynamic or the living situation. Just like I wouldn't criticize someone for not being attracted to someone not physically attractive to them. It doesn't make you shallow or selfish.
The thing is, everybody comes with baggage at our ages (yeah, you're a LOT younger than I am, but even at your age it's true). You don't find people without it after the age of 25 or so.
Look, you don't have to get married to the guy. I do think, though, since you are acting in the role of stepparent, and you are an adult in the home, you should be able to assume a parental role IN THAT HOUSE. There were a lot of things I disagreed with about how my ex and his wife were disciplining OUR kids. Stepmom was big on what I would consider bribery--paying the kids to hang up their clothes, for instance. But they were with them the majority of the time, and unless they were doing something I felt risked serious harm, I took the position that they had the right to do things their way in that house. I DID, however, let the kids know that *I* expected them to do what they needed to do without getting paid. And I insisted they do that. Yes, they were MY kids, but I certainly felt that their stepmom had the right to discipline them in HER home.
Kids can adjust to stuff like that. Obviously, if it's something BIG (like grounding them for life or mailing them to a remote country), you wouldn't want to do that without Dad being on the same page. But little things, like a time out or withholding a privilege, is something you should be able to do on an as-needed basis, without its becoming a major source of contention.