I have the same issue at my house although we do not share children together and mine are much older then his. We have my BS 19, BD 15 and SD 9.

You would think by the way both parents behave the sun rose and set by the childs whims. Because they have treated her in this manner the child has no desire to work hard for anything she is involved in. And BM has had her involved in almost every kind of activity you can imagine. They praise her when it is obvious that she is not intrested in an event she is competeing in even when she comes in last. News letters are sent out by BM on how talented she is and has even compared her to world class atheletes and Monet. She is rude to adults as she has been made to feel as if she is on their level. She is rude to other children as she thinks she is their superior. She demands 100% of the attention all the time. If she doesnt get it she pouts and throws fits. When I step back and look at the way she behaves she is just hungry for boundaries and limits. Children really need them and will continue to push until they find them.
Now my DH and I have been arguing back and forth over many of the behaviors of this child and the BM. All of my discussion that I have had, even when I can back them up with research, all come down to me being the bad guy. Me being the one that is to hard on his child. Mind you I have only scoulded this child in an angry moment once. The other times it has been, SD name, that is not appropriate behavior. I have had to completely back away and disengage from all of it. Still no peace as of yet...but I feel in time it will come. When these little "Princess" go through puberty Daddy will have to deal with the aftermath of what they have created. If you must use it as a learning experience with your own children as how not to behave. Reward them with proper behavior and let the "Little Princess" see what positive behavior recieves. This may get to be a little difficult because of jealousy and you do not want her to take it out on them. But stand firm and let your DH know what is going on. He will either get on board or he wont. But at this point you have done what you should in teaching your own kids.

not-your-mom...my story is very similiar to Bettina's and yours except she lives with us full time. She has the Princess complex and talks down to everyone...her father, mother, and grandmother (the one's who created her)included. I have never seen a more hateful, spiteful, spoiled, rude, self centered little brat in my life. She's one of these who has to get a present too when it is someone elses birthday...she acts like a 4-5 year old and she is 10. Constant attitude...expects everyone to drop what they are doing to appease her every whim. She absolutely does nothing chore wise and can (won't) do anything for herself...not even get herself a bowl of ice cream or a drink. Absolutely pathetic.

I am a very positive person usually but I find very little positive about this child...her attitude is so bad. She doesn't really like me...she tolerates me. I used to try and be a role model and show her right from wrong but it is a lost cause...she is so self absorbed that nothing else matters. I pretty much co-exist with her...Try as I may..I do not love her. I wish I could but I am not going to lie. I really love my BF..he is a good man but it is a very difficult situation indeed.

Take time for yourself...don't let it get you down or your BKids down or even other Skids that she may affect. Ignore bad behavior and reward good (hard in my case cause she is rewarded for good and bad mostly bad)...I hope you have better luck than me.