The one thing that's coming through to me loud and clear from this thread is that its not the kids that are the problem - its your DPs/DHs.
OK, I may be speaking out of turn, but I do have direct experience here - as a step daughter. And now as an adult looking back on the things I observed as a kid, and the bad stuff that I had to experience, I think so many step family problems stem from the fact that things between step mums (and dads) and their partners begin as many of you have described - you didn't 'look' for this situation, you 'just fell in love', you didn't 'expect' it to end up as a 'long term rel', etc etc. So, I'm guessing, by going into the relationship like that, you probably didn't sit down, by yourself and then in an indepth discussion with your partner, and really think and talk about what you were letting yourself/ves in for, and how the nuts and bolts of it were really going to work: the day-to-day boring bits, what the roles and boundaries are.
But you didn't get involved with a man who was footloose and fancy free, you got involved with a man who already had kids. They came first. Then you formed a relationship with their dad, got married maybe... and BAM... you know what - they're not 'someone else's kids' anymore. They are part of YOUR family.
It seems from reading all this here that what goes wrong with the step parenting issues you describe is not that the kids are 'brats' - its that they are confused, have experienced a lot of turmoil already, and their dads are misguidedly trying to make up for that by not providing them with boundaries, and by not helping you, the newest member of the family, with support and assistance to establish your role.
The kids are never going to go away, much as you might wish a 'magic wand' moment at times! Get to know them, you never know, behind all that rattiness and bolshiness there's probably a frightened and pretty nice kid waiting to be discovered. You might even end up being - shock horror - friends! And think how amazing it would be to look at them as adults and say to yourself - 'look at that person over there. I helped to create what they are today, and I didn't just do it because of a blood tie. I did it because I cared enough to make an effort to make a stranger part of my family'.