For your husband to offload the parenting interactions with the BM and SD onto you because "it is easier for him" (TM)

To be blunt, you weren't there with them in the bedroom , alleyway or backseat of the car when those two were spawning SD but you now are expected to be secretary, maid, cook, laundress, uber lift driver, hostage negotiator and bed buddy?  Not to mention financial backer of the failed first family.  

Very common but these men want SM to do the heavy lifting which is unreasonable at best and unethical as well as totally unfair to SM at worst.  You have 100%responsibility and most likely 0% authority.  

Please look into disengaging and shift the weight back onto your husband's shoulders as he is the actual parent.   And yes the high conflict, golden uterus, jealous,  juvenile BM will teach SD to hate and disrespect both of you.   Sadly that is what happens most of the time .

REmember: you do not have to let them treat you poorly. hand the load back to the parent. 

Look.. 12 year old girls.. teen girls.. can be the worst attitudes.. BUT.. they also can learn that a poor attitude means you get to live with those consequences.

When she is sour.. send her to her room.. "you can be in a bad mood.. but you won't inflict it on the rest of the household.. you can come out when you decide to act respectfully to everyone".

And.. YES!  it is "easier" for your husband?  well.. why does it have to be harder on YOU???   He  made the baby with her.. he can deal with her.  If BM is high conflict.. let him deal with her.. 

Have it easy taking on his responsibilities as a father.   Stop it, it's his kid ... He must teach her respect.  You are not her mother, you will never be her mother. Get that fantasy out of your head.  Your just her BF BFF.  He made her. Now he should parent her.

As a person who has no legal responsibility to SD.  [ If something happens to DH,  you will never see SD again ]. She must show you respect for what you are doing for her.  Or she can stay with BM. 

Disengage. Block BM on all platforms. You have to protect your peace. DH needs to learn how to co-parent with BM and not pawn it off on you. His kids are HIS responsibility, plain and simple. 

My SD13 sounds the exact same. Known her for 8+ years and the only way I can "deal" with the attitude is to disengage all together. 

What should you do?

Step back and place all responsibility firmly where it belongs - on your husband's shoulders. Your SD is being told that you are not her mother and that she doesn't have to listen to you. 

Your husband needs to get a grip and deal with this mess.

Disengage. Have husband interact and learn how to co parent or at least parallelparent. AND you need to hardline on the attitude towards you and provide consequeces. This is YOUR home and 12 yo Sd needs to understand that and understand that she will be held to standards of behavior or else!

Tolerate no lippy kid bullshit. Bring the pain and escalating abject misery.  Take her electronics the second she arrives and give her zero access until she leaves.  If she keeps escalating her shit behaviors, take her bed, take her door, take her makeup, take her favorite clothes, put her in baggy sweats, etc...

Keep escalating the misery until she pulls her head out of her ass. As for BM, tolerate no shit from her either.  Do what you can to keep her under the slime covered rock at the bottom of her shallow and polluted gene pool where she belongs. And... stop compensating for your DH's lack of balls and force him to man up.  Stop being his beard.

Sadly, far too many SM's are their failed family partners beard and bring "testicular" fortitude to the relationship that their male mate tragically lacks.