Welcome!
I think the first suggestion many people here would give is "go see a family counselor" but you've already done that!
The second usual piece of advice is "You can only control your own actions, but not the actions of others" and you seem to have figured that out already.
So, you have a good headstart.

I haven't gone through where you are (and hopefully never will) but I do know a few things about tween girls... I'm not saying this to excuse her bad behavior, but rather to show what she might be dealing with and help you see a fresh perspective when trying to find a solution.
The tween years (about 10-13) are really hard on girls. They're establishing social hierarchies and these are often REALLY harsh battles. Ever seen the movie "Mean Girls"? It's not far from the truth! She might be negotiating a minefield every day at school and taking it out on you and the family.
Tweens often face a lot of pressure from their peers to not respect their parents. But, ideally, the parents nip that before it gets out of hand. In her case, she's receiving validation from BD that she doesn't have to respect you, so it's growing and growing. She might not be "trying to drive a wedge into the family" but I can see how a tween girl trying to assert more power than she should have would be seen as that.
A lot of young girls idolize their fathers. It's pretty normal for a tween girl to think their dad is unstoppably awesome... But it's problematized when the pedestal they've put their dad on starts interfering with other relationships (such as with their mom or stepdad)
She's also a hormonal trainwreck at that age. I remember it, and it was AWFUL! I remember how every emotion felt enormous and made me butt heads with my parents sometimes too.

I know I didn't offer any solutions, but hopefully that gives you a fresh view of why she's being this way.

My daughter was BAD in 7th grade. She was nasty to me, I thought she would stay this way. Argued over everything, constantly showed disrespect, I used to cry my eys out. But then it all stopped. It is age.

She was never this way with her dad though, but I was a CP. He would tell me he does not know what i am talking about because not only she was nice to him, she also talked nicely about me in his presence.

Your SD is nice to her dad because she only sees him here and there, same with her SM. She is rude to you because you are right there! Unless it is going to become a serious issue, i would hope it is going to pass.

I'm sorry to hear what you're going through, and can hear how painful it is for you.

But as the previous two responders have already noted, that age is HORRIBLE for girls, and the family dynamics you've got going of "perfect" (but destructive) BioDad are working against you. The good news is that you're going to counseling, and hopefully, that will help.

I imagine one of the early things the counselor will say is that Mom needs to firmly and immediately enforce a "no-disrespect" policy towards you. And also that you and your wife devise a short list of clear and unambiguous "house rules" with well-defined consequences. Then have a family meeting where Mom presents these rules - post them in a conspicuous place - then you try to limit your discipline of the girl to issues on this list, disengaging from the rest. (If the counselor doesn't suggest it, I'd ask her about it.)

If you can stick with the counseling and continue working as a team with your wife, I'm betting that things will be much better in 2-3 years.

I think Sweeby is right on. Mom really has to get involved here, regardless of how her daughter treats her. The two of you are a team, and you can't play together when you each have a different set of "rules."
Expectations need to be set, and she needs to be the primary one to dish out the discipline. This doesn't mean you take a back seat and get walked on, but if the two of you are together and something is said/done by SD, mom needs to be the one to immediately step forward and shut the behavior down. This will show the girl that she is being disciplined because her actions are disprespectful, not just because she pissed you off. It's then less about the dynamic between you too and more about her behavior.

Aside from that - tween years suck for girls. I am the custodial SM to an almost 13 yr old girl, and I know first hand how difficult it can be. Keep with the counseling, and keep your chin up. I keep hearing this will pass, and I'm clinging to that . . . .

Best of luck, and keep posting.

Everyone is right, part of it is the age. This happens in homes with both natural parents living in the home. She is testing the limits, and your authority. However, it needs to stop, because as the oldest child, she is setting the tone in the home for the two younger children, and how they talk to you. They are so young right now that it may not be harming them yet. But 4 years from now, she will be 16 and could be very difficult, and your 8 year old child will be watching and learning.

So I imagine it is finding something that works, in teaching her that regardless of what her father tells her, this is your home, and you pay the bills, and you will not be disrespected in your own home. Period. I have a friend who had a similar situation. The time outs in her room did nothing to change the behavior. This woman is a wonderful cook and her daughter looked forward to the wonderful dinners she made. One day, the pre-teen was again very disrespectful, and while the rest of the family ate the wonderful meal, she ate alone, and was only permitted to have cereal and water, and was sent to bed until the next morning. This was only done that one meal, but they said they would repeat it again, if the disrespect showed up again. I imagine she will test them again, and again, she will learn now that they will be consistant in showing her that she will not treat them that way. This worked for her because she loves her mothers cooking. some kids are picky eaters, and it would not work for them. Oh, and All electronics were taken away that night, and have not yet been returned.