You are not her biological parent.  Your DH should be parenting his kid.

HOWEVER.. you are also HIS partner and joint head of household.. so you do get a say in how the household is run and boundaries and standards of behavior that are expected of its residents (ie SD).

Now.. that doesn't mean you are the enforcer.. but you do have a say.. you just should not be the one driving the parenting bus. 

Of course, it goes without saying that if you don't have the power to manage his daughter.. she should not be there without his presence as you can't discipline... so he will have to figure that nut out.

Cyfd have no say in disipline or decisions that have to do with her either, unless there is evidence of abuse/neglect. Your husband is welcome to talk with you about issues and work with you to find rules and consequenes that work for your home. With a 15 year old that does not like or respect you it is probably best if her dad does most of the disciplining and makes a show that he has final say even if he consults with you over these issues. 

In general, stepparents shouldn't discipline their kids, the bio parents should, IMO. He needs to step up and parent his kid.

Fuck your SD and her manipulative demands. Im so sick of the skids(mine and many others) who are products of divorce and play this game. My sd17 is mad at her mother for abandoning the 4 of them years ago and she takes it out on DH and now that I live here for the past year and half she also takes it out on me. Mommy dearest (BM)  drove off in a moving van with her new boyfriend and left her 4 children behind and all is forgiven but if I breath too loud she "cant live with me".

Your sd got her nose out of joint. Because she doesnt like your form of discipline. But the thing is when your a responsible adult and you see a kid doing something wrong no matter who's kid it is  you need to nip it in the butt. Maybe give the final discipline action over to the bio parent. But sometimes you cant just stand there just go do as you please because im not your mum. Because if something goes wrong and she in your care. Who gonna be at fault??  YOU 

Touchy area?  Sure.  However, I would seek a lawyer as an agency should have no business saying something like this.  Furthermore, I'm in total agreement with the child centric mess this country has become.  Have a come to Jesus with DH and attempt to get the two of you onto the same page.  If he refuses and backs the insane demands of a Child, then leave him until he will come around  

Then you can not be alone wtth SD.  DH must always be there.  You must set up house rules and SO must inforce the rules.  Or it's time to leave.  You can not live in a home where SD has control of 

?

Two options:

1.  Disengage completely  (good)  https://steptogether.org/help.html

2.  Leave the situation completely (better)

Under those circumstances, I would tell her father that you can't be alone with her, so if he's not there, SD doesn't come over, and he is fully responsible for her. I would totally disengage, too. No rides, no doing her laundry, etc. She and her father can't have it both ways - you're either in or you're out where she's concerned. What is her custody schedule?

Also, you CAN have a say with what goes on in your home. If it concerns her it can just be decided/discussed with her father and he has to communicate your "mutual" decision. No government agency gets to tell you you have no say in your own home.