L.L.
I have a soon-to-be 20 year old daughter, so I feel your pain :) I think it's great that you're taking on the responsibility of raising your step-daughter and seem so concerned about raising her correctly! It sounds like her mom isn't so top-notch and maybe your step-daughter is craving some order and structure (kids all need it, no matter how much they complain).
It sounds like you will be the primary "mother" in her life, so it's up to you to set the boundaries clearly. I would start by discussing your discipline plan with your hubby, that way you're both on the same page (about consequences) when the problem behaviors occur. Then sit your step daughter down and explain the rules to her. I always believed in explaining the reasons behind my rules.
My daughter and I had MANY fights over appropriate clothing! She was in middle school when the tank top craze started, and it seemed that each top got tinier and more revealing! I tried to come to a compromise by taking her shopping and relaxing my standards a little (and explaning why the trashy clothes were not coming home with us), while letting her buy some "cool" stuff. I would, however, put your foot down about the Britney Spears outfits :) Plus, I'm sure your daughter's school has some sort of dress code that bans really revealing clothing. You could check and back up your rules with school policy...there's nothing more embarrassing to a budding teen than being called out in front of friends!!
I also made a chore chart for my daughter. I know, it seems a little juvenile, but a lot of teens or soon-to-be teens are not great at responsibility or remembering to do what you've asked. I also posted this chart in a prime spot in the kitchen, so there were no excuses about not seeing it. Believe me, your daughter will find every loop hole in every rule!
You and your hubby should make the house rules clear and be consistent with enforcing them. Your step-daughter probably isn't used to much structure, so be patient. Nobody said raising teens (or pre-teens) was easy or fun, but there is a light at the end of the tunnel :) I think my daughter is a really fun person to be around now (2 years ago, not so much), and her friends are great!