Start taking things from her that she leaves around.  Don't give them back. That should soothe the inner beast.  
 

 I'm glad the therapist pointed out two different parents= two different styles.  It sounds like BM is projecting her own less than childhood issues on to SD.   Our HCBM did the same thing.  Parallel parenting talk is needed IMO.  It reinforces the differences between the two homes and gets rid of the upmanship games that BM is pushing.   DH should be able to be accepted for who is is, just like SD is demanding it for herself.  If he does start standing up for himself, they will escalate the drama but he needs to hold tight while they learn he means it.  She is 13, dads need to  encourage independence, not coddling.  Her mom can do that for her.  
 

BM is still way to deep in your lives for my taste.  Drama from SD keeps her relevant.  In our case we called BM out in her games and intentions.  Things died down after that.  Our therapist treated us as if we had encountered a Cluster-B nut job.  ( unable to diagnose BM)  

So many of these teen SDs on Steptalk remind me of SD61 as a teen.  Entitled, spoiled, needy, manipulative.  But the endless desire for entertainment drove me crazy.

DH was very active with all 5 kids and especially sensitive to "poor"  SD.  He felt so sorry he bought her a horse!  So we suddenly had a new expense for equipment, boarding, vet, etc.  Whatever, he was paying for it.  So on weekends, he'd take all 5 kids to the "ranch".  I sometimes went.  One hot day, after spending all day in the heat with 5 kids and the horse, I couldn't wait to get home, take a bath and lie down.  That's when I heard SD say, "What are we going to do tonight?" Smh.

Actually, the thing that helped was her bringing a friend.  Things seemed calmer then.

I don't get how it became a parent's job to entertain their kids. Sure, on special occasions we would go places and do things, but as a kid 90% of the time i played with my sister, my friends, or did things by myself. On vacation we would do entertainment things together. I think it must be a child of divorce thing. I don't remember anyone whose parents felt pressured to be or provide their kids' entertainment. Food, clothing, shelter, education, and even supporting extracurriculars, yes. My parents bought me toys but they didn't play with them themselves. 

Yet refuse to see they also contributed to and caused the very issues they're complaining about.

for example my eldest sd sulk called daddy crying on the phone as a 23 yr old about how daddy abandoned her and her sister to marry and have kids with me. Ignore the fact she and her sister willingly disappeared and cut off all contact with their dad over lies they knew their mum made and when biomum abandoned them, never did they call daddy for support or help.
 

5.5 yrs the cut off contact and disappeared then had the nerve to blame and guilt my husband for moving on. Ignore the fact that sd's continually cancelled last minute any plans and outings we had, we were expected to cater to their every whims or say they were busy. Now you complain when daddy would rather spend time with his wife and 2 young kids. Its not rocket science when you make outings so unpleasant that your dad now has his wife not wanting to spend time with you and his weekends off he wants to spend time with his wife and kids with her and since you wanna be unpleasant and ruin the mood, he doesn't wanna miss out on time with us so unless yoy can be civil and comply, there is no special time with you at expense of not spending time with us. 
 

too many skids here complain stepmum is so horrible and won't allow a relationship with their kids and skid yet skid is such a toxic person you need to stay away from but would rather blame stepparent for their bad relationship with others.

its mindboggling stupid at times but I don't tolerate toxic petty bullshit like this. Life is too short and precious to waste on people like this

I, too would make a list of all the things I didn't like about her, just to show her she isn't the only one who can hyper focus on the things she doesn't like. Then I would ask her to write a list of what she DOES like about being around, just to push it further. 
I'm sorry but reflecting back on my experience, I wish I would have addressed poor behaviors more. I used to always tell the SSs that they were not entitled to anything about me. I tried explaining to them that the one who is obligated to them is their mom. This is why I had to sort of force DH to get SS out and into jobcorp. He's 18 already, and I've been telling him for years that he won't be able to stay living with me while having the attitude that he can do as he wants, just because his dad lives with me too. 
I'm projecting but phew, one needs the patient of Mother Theresa to deal with these kids. 

At age 13, surely most kids want to do stuff with their peers, more than their parents, don't they? I know I did. Having said that, DH was always taking his daughters out to do stuff, up until their late teens - I call it infantilization, personally. But of course they were only too happy to have him spend endless £££ on them!  

It blows my mind that a 13yo even thought of drawing up a list of complaints like that, not to mention the skewed view she has of the world. On what planet is it OK for a child to yell at a teacher? Gawd, she's going to have a rough adult life if she doesn't get over herself soon. She'll never stick it out for studies and who is going to employ someone who thinks she gets to decide how and if things get done? Seriously?

I remember many times when we would take her out to things, she made certain to tell us when she was "bored". Eventually I got p!ssed and told husband that it really was selfish to say that, and made me not want to take her with us, she can stay home and be bored for free...he got it and I could tell it irritated him too.

Of course Ive stepped way back, but when she was talking to me about how upset she was that her mother is not allowing her to get a job, so they can stay in the low income 2 bedroom apartment in Beach Town, I couldnt help myself "I guess its a sacrifice, so you can live in Beach Town..."

Its frustrating knowing where these things are headed. I dont know how you keep your cool.

out with me much anymore but really that's normal.  They are supposed to have full lives with friends and activities.  The whole point of raising them is to set them free as self reliant productive happy adults with lives of their own.  I hate, hate, hate codepency.  I think its insidious.   

I can't imagine giving my parents a Perfomance Review when I was a kid. I'd get slapped into next week.

I hope this is the last time DH entertains this nonsense. He's training her to give voice to her bullcrap. He needs to de-platform her.

It's a pet peeve of mine when kids complain that their parents don't do enough "things" with them. Since when was it a child's right to be entertained and showered with gifts and outings every moment of every day. I remember once we went to a pumpkin patch. We bought pumpkins (which were super expensive and each kid got to pick his own pumpkin without any size limits) and then let skids pick one activity. They picked the corn maze (which was not free), so they did that. Then after, one SS said, "I can't believe we came here and only got to do one thing!" We had spent over $150 for pumpkins and two kids tickets to the corn maze, but it was apparently not enough. When skids went out to my home state, they went with DH and my dad to this ice cream stand that also had an activity park. I remember my dad being horrified that DH paid for both kids to do every activity at the park (mini golf, bumper boats, batting cages, arcade). He couldn't believe how much money DH spent, We would have gotten an ice cream and maybe played mini golf, but that would have been it. It's so entitled and I wonder if it comes from mothers who are always telling their kids, "your dad doesn't do enough for you!"

the intent on clarity for SD.

In detail. For countless hours. No delay for tears, whining, complaining.

Bare her ass one square inch of skin at a time until she has had her nose rubbed in every bit of her teen toxicity.

If that does not stop it, do it again. And again, and again until she launches.

At some point.... kids need clarity and appropriate effective consequences in an age appropriate manner. 17 is far beyond old enough to have her as bared for her toxic crap.  A 17yo should also not be allowed to hide behind a therapist.

That kid needs her nose scrubbed in the stench of her toxic behavioral choices.  

Lather... rinse.... repeat.