I'm new here folks, so bear with me, please.

I met my fiance (I'll call him 'K' since I'm a lazy typist) online about a year ago. Last June, I packed up everything I owned and moved lock, stock and barrel from the US to the UK to be with him. Our relationship is wonderful, he's the best man I've ever known, and I have no regrets about moving there.
But (there's always a 'but'- isn't there?) 'K' has two children. A girl 13 years old and a boy 6 years old, along with the BM. The son is fairly accepting of the situation, but the daughter and BM are another story.
Let's start with the BM. Evidently, her idea of being a good parent is to give the kids anything they want, to set no rules for behavior, to allow them to speak disrespectfully to anyone they please, and if they act out, to send them to spend the night with a friend. As far as I can tell, she does absolutely no disciplining of the children. They have never been required to do anything as far as helping with keeping the house tidy, are allowed to eat exhorbinate amounts of candy, crisps, chips, and sweets of all kinds, and rarely see, much less eat, a vegetable. When 'K' goes to pick up the kids, he is given his 'marching orders'- everything from what we are supposed to cook for meals to where we're supposed to take them during the time we have them, etc, etc, etc. She calls me 'that woman' and 'K' has been informed that I am not to 'discipline' her kids (keeping in mind that telling SD 'no, you can't have another bag of crisps' is disciplining her). She is extremely controlling and expects that when she tells 'K' to jump, he should ask 'How high?' If we don't follow her rules, then a 'family meeting' is called (to which I am not invited) and 'K' is expected to explain to her why. I could go on, but I'm sure you get the general idea.
So on to SD. She is mouthy, sarcastic, defiant, and rude to everyone in the family. (Yes, that includes her mother) She has no qualms about calling 'K' stupid, idiot, etc, and has a sarcastic answer to every remark made in her presence. She expects everyone to do her bidding, and if we tell her no, throws a huge fit. She's already informed her mother that she is going to do everything she can to make my life hell. If 'K' or I make her clean up after herself, or tell her 'no' there's another fit, and usually a call to 'mum' complaining. 'K' and I have set rules, and make her follow them, but spend most of the time she is with us having to deal with the attitude and the screaming fits. Both of us spend the whole time counting the hours until she goes back to BM's house. And of course, 6 yr old SS is starting to pick up on the attitude too.

I could go on and on... but I think that's enought to start with lol. So, any suggestions?