I have a 16yr old DS, and DD's (6&3). I totally understand what you are going through.
I totally agree with setting limits calmly, using toddler style rewards and sanctions.
My rewards tend to be film nights (without the girls, so not restricted to Disney!) foods that that the little ones won't eat, alcohol free cider, playing x-box with him (aaaagggghhh). Sanctions are limiting phone top-ups, online time restricted, refusing to give lifts (we live rurally, so not grounded, he just has to use his legs/pocket money to get places).
You can set passwords and time limits on most routers, so it even limits time spent on iPods etc.
If he leaves dirty clothes/towels lying around, they end up on his bed, if he leaves school stuff etc lying around, they end up on his bed. His room is his responsibility, usually it is a pigstye, but occasionally he tidies and hoovers! He has been taught how to use the dishwasher and washing machine, and does so occasionally. If he wants to cook for himself aside from the meals I cook, he tidies up after himself, though he is still crap at dealing with breadcrumbs and sugar on the side. He can and very occasionally does clean the bathroom, he walks the dog most days.
A year ago he refused to do anything, had temper tantrums in massive proportions which included throwing mainly his belongings around and smashing things up. He was vile. I was angry and digging my heals in. Learning to pick battles is absolutly vital. Fighting them in a calm and mature way is the way to win.
I would suggest laying out your reasonable requests of her behaviour while she is living with you (washing her own dishes that are not part of a family meal, putting her laundry in the basket, minus dirty sanitary products, if she would like you to wash them, or do it herself, take a turn at cooking, take a turn at specific cleaning jobs - you sound as busy as me, so a rota might be a good idea? And anything else that you think would be reasonable).
Give her the option to comply with these, if she is not happy with it then she is welcome to go and live at her dad's -her choice, not you chucking her out- and would be welcome back at any time, but she would still be expected to live by your rules. Make it clear that if she says she is going to stay with you but doesn't actually get her arse into gear, she is effectively telling you that she has chosen to live with her dad, and you will take her there, or get him to come and collect her (whichever is easiest for you).
I suspect you may have a screaming fit from her, but if you stay calm and stick by it you may get a few days/weeks(?) peace until she has had enough of step mum, or step mum has had enough of her!
Good luck, and let us know how you get on