"We have explained her time and time again that thw longer she drags this out the more hurt we are all feeling and if she is honest it will hurt people less then her not being honest." This indicates that you and your partner have placed your feelings into this little power tripper's hands. She's been granted way too much power. She's drunk on the power of being able to impact an adult's feelings (making you cry and withdraw to another room and believe me, she knows it even if you say you hide it). Telling her that she's hurting people more by not telling the truth is reinforcing her ability to control the adults around her like puppets. It's time the adults take their power back. If you and your partner don't know how, then go for some counselling to learn how to parent. There is nothing wrong with that. My DH and I knew we were f*cking up with our DD20 (when she was 15), so we went to counselling and changed everything after only three or four sessions. We had a couple of follow ups and that changed the course of our entire family and marriage. 

Your partner is failing as a parent and as a spouse. Telling you to just put up with it is dismissing what you're going through. He's a craptastic partner, so I'd have it out with him if I were you.

Your partner is dead wrong when he says that your SD will soon realize that she isn't getting her way. She IS getting her way. She's doing what she's doing because there are no consequences. When she sticks to your SO like glue and asks assinine questions, he doesn't call her out on her manipulation tactics. She should be consequenced. When she acts miserable to the family and pulls the "I miss Mummy" card, she should be called on it and consequenced. It's time for progressive discipline. The good news is that you and your SO know her currency: her tablet. She should lose the tablet and all other electronics opportunities for longer and longer each time. It will get worse before it gets better because the longer she has gotten away with this crap, the longer it will take. Also, she will pull quite the number to make it look like it's not working. Maybe full on melt-downs, suicide threats, "I don't feel loved," and on and on and on. As painful and hard as it is, I had to stand strong when my stubborn mule DD pulled every tactic out of her bag. DH's and my counseller told us to start instituting consequences because "talking" to her or "waiting it out" wasn't working.

Kids do not ever grow out of stages. They do not mature on their own. They have to be required to mature and they have to be parented through stages. When their behaviour is bad, such as your SD's con artistry, it's time for consequences. When our counsellor talked to dd (we were asked to bring her to a session) she even told all of us that she would prefer consequences because the constant talking to her felt like nagging and it was annoying. Consequences were preferable to the "nagging." Who knew? LOL

Your partner needs to do some self assessment to figure out his reluctance to parent your SD. Is it because he's afraid of losing her? Is it because he's parenting from guilt? Or is it simply that he doesn't know what to do? Right now he's failing all of you. You, his spouse, are suffering to the point of frequent tears. The other kids are suffering. Your SD who is committing the behaviour isn't going to want to grow up to be a cow. People aren't going to like her, if they don't already. Your partner is probably suffering because he wouldn't want to see his own DD be like that. The whole household is being brought down by a child and your SO is allowing it. 

You can take charge by telling your partner that he either needs to start parenting his kid and consequencing her to start resolving the strife in the household before the sun sets today or he's going to have to get an apartment for her visits. You are 50% of the adult equation of the household and the woman of the household. You are every right to take charge like women of their households.   

May Rags can chime in with his wise "lather, rinse, repeat" comments. Those are golden!

You are being played by PAS.  Everything was fine until BM realized they came back to her happy.  That's a sin you know, eyeroll.  I do think you moved in too fast and were blinded by the Brady Bunch fantasy.  

I think there are three separate issues here the each has to be addressed.

First, your BF needs to start giving consequences for this behavior. She's upset that she lost her tablet? Fine, she can go be upset by herself in her room. She'll scream and cry at first, but then she just needs to lose the limited tablet time that she has. The behavior is a pretty standard tactic that most kids use to try and get their way. If he can't handle that, and his "solution" is to send SD away because his GF told him to, he's a crap dad. 

Second, and I'm not sold on this idea based on the information provided, BM may be trying to poison SD against you all. Sending SD back to BM only confirms any BS BM is feeding SD. Your BF needs to handle this in his own home, perhaps by getting his daughter into therapy. I'm not convinced PAS is the problem here. I think BM is just a permissive (and possibly absent since she dumped SD on the grandparents) parent that gives in to SD, and SD is trying her luck with dad, too. It has only been a month or so since this started, so there is plenty of time to try and fix this.

Third, I don't think you're cut out to be a SP if your reaction to a bratty kid being a bratty kid is to hide in your room and work yourself into panic attacks. Nothing you've written makes me think "dear god, SD has a serious mental health issue and this is going to be a real bumpy road". What I read is a kid who has had some major life changes in the last 18 months with Dad getting a new GF, playing family with a new person, and moving in to a new house WHILE in the middle of a global pandemic that has likely sickened or killed someone she knows and has seriously changed how she goes to schools, when and where she gets to see friends, and just what is permissable to do in the world. That is a recipe for a kid, especially a slightly older kid that is starting to form the reasoning part of their brain, to start having behavioral issues and it be totally expected.

Both you and your BF need to get your heads out of your backsides and deal with the situation at hand. You need to tell your BF to fix the problem, not ship it off somewhere else to be ignored. Your BF needs to address the problems in his own home with the plethora of tools at his disposal. You both need to figure out how to handle adversity in this blended family because this is SUCH a minor problem that not handling this spells doom for yoyr relationship. You need to do some soul-searching on whether you can handle this or not, and whether your BF is actually a good parent. Like you alluded to, you can't keep the BF but toss the kid. If you can't handle typical bratty lid behavior AND he won't address typical kid behavior, then end it now before you invest anymore time.

Electronics are a bona fide addiction, and it sounds like she is bored because she doesn't know how to entertain herself.  Specifically let her know that the word for her problem is "boredom", and she needs to learn how to entertain herself.  Make sure she has books, art supplies, tv, games, and toys.  Maybe let her bring a playmate for the weekend.  Maybe teach her how to bake, and let her make brownies.

If she's staring at you or pouting, send her to her room, or send her outside.  Being uncomfortable and retreating to your room rewards her bad behavior and compromises your authority.  Assert youself by telling her to "go play".  Tell her if she can't find anything to do you can find her a chore to work on.  Be prepared to follow through on that.

Killjoy used to do that thing where she'd pepper us with stupid questions all day in a demanding voice, like she was entitled to grill us to her heart's content, blurting out stupid crap without thinking about anything.  It was a power trip for her, and attention tactic.  She'd act like a victim if we refused to answer.  It pissed me off so bad.  We started shutting that down.  Literally, sometimes she got, "Wow, that was a stupid question.", or "THINK ABOUT IT".  If she asked a reasonable question, we'd answer.  Then she was allotted 5 questions per day, and told not to waste them.  In the end, her narcissism got the better of her, and she was so afraid to ask stupid questions, she stopped.

Wait.. your BF took her back to mom's because she was "bored and said she missed her mom"? wow.  Why isn't he parenting her.. why is she just staring at YOU?  why doesn't he take her out for a walk.. play a board game with her?  find an activity to do with all the kids and insist she join in? 

He just says.."oh well.. back to mom's you go"?

She is a young girl.. she doesn't get to make these choices.. her father needs to be a parent and help her work through frustrations.. 

Oh.. you miss mom?  Well.. we miss when you aren't here too... come on.. let's go do something to take your mind off it.

You are giving her all the power. Take back your power.

Your partner needs to parent his kiddo. Dh always does that "kids not behaving, ok, she can go back to her mother, see how she likes it." Drives me nuts, and thats not the answer. I just think after dealing with Toxic Troll for so long (going on almost 30 years), and trying to parent for over 20 years, hes tired of fighting and has no more fight left in him.

But in your case shes still very young. Shes power tripping. Even sending her back to her mothers because shes not behaving is a power trip for her, because she gets to dictate to you, the adults, what she wants to happen.

STOP THAT RIGHT NOW.

But honestly, time to evaluate what you want in this relationship.