1.) Your SD is in a loyalty bind. She knows her mother will make her life hell if she doesn't go along with what she says, so she says it. At 11, she has another 7 years at least of dealing with her mother painting you all in a bad light, breaking court orders to keep her from her dad, and probably being punished if she doesn't perform to her mother's liking. Either SD recognizes this all consciously and is playing the long game until she can cut BM out of her life (less likely) OR she will get sucked into BM's world because the level of psychological trauma she is being put through is easier to just fall into than to accept, meaning she is and will turn on all of you (most likely). Kids don't hate good parents for no reason. There is a reason she behaves this way, even if your DH isn't at fault but paying the price.

2.) If she is going to visit your home, I highly suggest nanny cams in common areas so you have video evidence that SD is not being abused. Bonus if it shows SD having boatloads of fun with you all. This is less a tool to be used in court by your DH to get custody, and more a tool to protect you all from future abuse allegations.

3.) Read up on disengagement, and disengage from SD. This isn't punishment toward SD; it's peace of mind for you. Since you have other children and your DH is going to be understably conflicted about his daughter, one of you needs to be level-headed and less stressed. Let that be you.

4.) Your DH needs a therapist who specializes in parental alienation to help him through this. He needs to be preparing to lose SD to BM, especially if the courts don't side in his favor. Mentally preparing to lose his daughter will help prevent him from putting you all in the poor house due to legal fees and help him create boundaries around himself and you all before her behavior ramps up further in her teen years. He can learn to enjoy the happy time he has left before it runs out.

These types of situations are insidious, and parents who put their kids through alienation have a special spot reserved for them in the afterlife. I'm sorry you're going through this, and I'm sorry for SD that her mother cares more about herself than she does SD.

My SS did this to us as well. Our lawyer put him on the stand and questioned him in front of his dad. 

We had pictures of him smiling and happy and the lawyer would ask about the events happening- it contradicted everything in the letter. It was very telling and the judge ordered that visitation with dad would continue. (Not that it helped in the long run, but it was good in court). 

It all comes down to how much you want to fight for her. 

Wow we are living very similar lives! Right down to the age of the stepdaughter and the two kids of her own. I have seen a similar thing happen though my husband had a custody arrangement in place before we got married so we didn't have to worry about that, not that BM ever followed it but we weren't going to court. 

My SD 14 also seems perfectly happy and pleasant when she's with us and seems to hate us when she's with BM. Like others have said she is probably just saying this to please her mom because she's stuck with her mom a lot more than she's with us. It definitely got worse when we moved in together got married and when we had each of our kids. Contact with SD reduced more and more each time. She won't even answer the phone or reply to a message most of the time anymore. 

It's okay to just let it go. Focus on your family and on the rare occasions that you do see your SD just treat her at face value if she's pleasant to you just be pleasant back the visit will be over soon! You and your husband need to just ignore everything negative coming from BM.

Shes being put into a loyalty bind. I would definitely get nanny cams and journalise and document. And then get prepared for the worst. Please do not gt yourself into debt fighting for years and years. Even if you "win" you could still end up losing, so many stories of winning the battle and losing the war (the kid).

Just get emotionally prepared, and disengage.

BM was probably standing over her telling her what to write. When SD is with BM, she feels like she has to go along with her in order to survive. All this stress will probably cause SD emotional problems. It's sad. Kids in these situations don't learn or mature properly because the energy that should go into teaching and guiding them is instead going into all this drama. It's like the 5-year-old in the other thread who only knows like 10 letters. She may be "normal" but there's not enough brain space to deal with drama and to learn and develop at the same time. Don't take any of this personally. You didn't create the dysfunction, you can't fix the dysfunction, and all you can do is try not to be sucked into it. 

I am in the UK and my ex is currently dragging me through court as I have stopped him having unsupervised visitation due to domestic violence which he conducted in front of dd6.

Do NOT film your stepdaughter and any interactions she also may have with BM while she is with you, without checking with your solicitor first. British courts take an *extremely* dim view of recording evidence and while it is not illegal, they likely will get angry about it and it will not bode well for how they and CAFCASS view you. Obviously I am in a different situation to you, but even security cameras filming for the basis of protection would not be accepted, in my case (and even my barrister echoed this). So be careful and check first.

All of this stuff is just tiring.  I dealt with the same things for years.  These BMs bring up entitled kids that call the shots.  If you take the high road, then the PAS will win out with the kids because someone is always undermining your family's realationships.  You can fight like hell and go bankrupt, and it still won't make a difference.  You end up with stepkids that resent you and live for every word that comes out of BM's mouth.  They may realize later on what she is doing but they will likely never admit it, and it really won't matter at the point.  The damage is done.