Get up and leave the house before he does. Do things that give you pleasure. Tell him that you're not doing it any more, that the kid is his responsibility and he doesn't get to shirk it. 

Also, don't be afraid to speak up when the kid is rude. If a teacher can do it, YOU can do it - in all cases. 

I am sorry, but this will not change. Time to cut your losses and exit the relationship.

My SD14 can be snotty and rude too the only reason that she is tolerable is because we don't have her often and I'm never personally responsible for her. If she was getting dumped on me like you were SD is dumped on you it would be a totally different situation.

10 is a tough age and this is about the time that BM had it with my SD as well. It just became a personality crash between two b****** and she wanted us to have her a lot more often. As you said it was not your mistake and she should not be your problem. Do you get to go out and socialize with your friends and do your hobbies? Or are you just enabling your SO to be able to enjoy his life at the expense of yours?

Before the weekend even comes tell him that you can't watch her you're busy with your own business. Give him time to cancel on his friends. If he throws a fit and insist that you watch her then say that in order to be able to handle watching her while doing your job you should get paid for providing child care. You are doing him a huge favor don't let him take you for granted.

If your SO leaves to hang out with his friends, pack the child up and take her to the football (or whatever) and hand her over to her parent.

You do not have to look after someone else's child.  This is not your job.  It is the responsibility of the child's parents.

Anyone else had a similar situation and if so how did you deal with it

No, my DH did not allow such behavior from his child and never dumped her on me. I would have absolutely NOT dealt with it.

Your partner is not much of a parent or a partner.

I have never babysat my SDs, not even for half an hour, ever, nor would I have agreed to it.  It is not your job to do this, just refuse.  If your partner plans not to be in, then he can either organise a babysitter, or the girl doesn't come.  As to her behaviour this is also your partner's responsiblity.  He should be challenging her and asserting his authority.  He doesn't because he is a rubbish father, and it will just get worse as she becomes an adolescent.  I wouldn't put up with anyone annoying my dog - I would bring the wrath of the goddess down on her head, she would never do it again. 

Every action you described is completely manipulative. She's not a lazy slob. She is well aware that her behavior irks you, so she will continue to up her game until she's certain you know she has "control" when she's around. If you and her dad are not able to cooperatively establish rules and boundaries, well, it ain't ever getting better. 
My SD10 is ultra manipulative, and although her dad will bust her occasionally, he truly believes she is nearly perfect. He always believes her explanations of incidents over my children because she is "the oldest." I could go on and on, filled with fire and rage. 
I try to remind myself that she is just a kid --a kid who annoys me to my core --caught in a less than ideal situation, and I have 30 more years of practice at being manipulative under my belt!