If I'm not mistaken, you had the thread about BM giving gifts to DH? So, I hope I didn't get that wrong, and here's my take.

When my DH & I started to get serious, BM started to unravel. She all of a sudden started having soooo many problems with SD's behavior that she was using that as a reason to call DH all the time. And SD was acting up with us too. I think it had to do with our relationship getting more serious and her being upset that she was losing daddy, etc. and it could also be that she saw how her mom was acting over it too). BM wanted to 'get together' with us to 'talk' about it... but never followed through. Instead, she would call DH several times a day. She wanted SD in counseling with all of us there, so when she didn't arrange it, I did. We went & she tried desperately to get them to diagnose SD as ADHD so she could be put on medication. We (DH & I) decided that we had to be more consistent with SD and within a few weeks, her behavior had calmed down (she got away with NOTHING) and as her behavior improved, she got more rewards. BM was still complaining that SD won't behave for her and in talking to SD, we found that BM was very inconsistent with her. She didn't have a routine, they ate out most nights in different places. They went to visit friends whenever, so she went to bed at different times every night. Sometimes it was okay to be rowdy but other times, mom didn't have patience for it so she'd get in trouble. She really doesn't know how to behave at mom's house so we realized it is MOM'S problem. DH told her what was working for us and suggested she make a routine & stick to it. He also suggested parenting classes and put it on her to figure it out. It's her responsibility, not his.

The most we do now is tell SD that she should behave at mom's. (and if she comes back with a report from BM that she did something really bad, we continue whatever 'restriction' BM starts, if any. That way, SD knows that we support mom in getting her to behave. But, how mom deals with it is her business. (of course now mom lets her do whatever she wants there so there is no complaints lately. She only sees her for weekends and DH thinks when she has her for the summer, she won't be able to handle SD... who knows?) You can only control what happens in your house and your DH can't be responsible if BM can't handle it.

"So what's really going on and how can we fix this."

You can't fix someone else's problems.

I totally understand everything you just wrote. It makes a lot of sense.

I guess my thinking was if she can't do it, then how do we set a different standard for SD. My belief is that if she keeps doing that stuff w/BM, she'll test everyone and it will lead to other problems

Hi there! I've been a SM for almost 9 years now. Our situation is very similar to yours. BM complained about SD since she was 3 (she'll be 10 in June) and we've seen so much of the same behavior; good at our house and a complete monster with BM.
BM has doctor hopped (let me mention that she is also an RN) until she found a doctor that will work on SD's behaviors. When SD was young BM and I got along and worked alright together and since I have 2 older children of my own she would ask questions and take advice. We were then pretty close for 3 years and now the past 2 she's gone on a "I hate the SM" spree. We only suspected that BM was saying things to SD 9 about us until two months ago when BM had a complete melt down at the local grocery store when SD saw me and wanted to come see me. (I'll post about that later). My DH deals with BM calling him at all hours with SD SCREAMING at her and flat out refusing to do anything BM says. We also see no structure in BM's home. SD goes to bed whenever, gets grounded and then rewarded all in the same day, is bought whatever she wants and regularly goes out for breakfast, lunch and dinner with BM.
DH is trying very hard to be involved in the counseling that SD has even though we strongly feel it is BM who needs counseling or parenting classes to learn how to say NO. The kid doesn't pull any of that crap here. She may get snooty from time to time but she doesn't scream or pitch fits in public or tell us NO. We go out a few times a month as a treat for the kids (we have 4 at home still - DD 16, ODS 14, SD 9, YDS 7), we don't buy the kids something every time we go to the store, and they have regular bedtimes (BM takes SD out to restaurants at 10pm on a school night regularly). SD is her "best friend" and frequently gets manicures, pedicures, full body massages and any pet she wants. BM also says that we don't have accurate chores for SD to do when she's with us EOWE. At 9 I believe picking up after herself, helping clean the bird cages when she's here, making her bed and putting away her clothes/toys and helping set the table are enough. BM doesn't agree but oh well, it's our home.
I truly don't know how you can change how SD's BM deals with her. We have yet to have SD test us though her behavior with her mother has gotten worse. Be consistent, let your SO talk to the child and tell her that treating BM that way is wrong. Let him listen but don't let BM have too much control over SO. He needs to understand that BM has to get it together and parent the child. Kids push mom's buttons more than they do dad's. I haven't met a child yet that doesn't. Have SO recommend timeout for BM and SD when the child is acting that way. If BM is consistent (which from reading it doesn't sound like she will be) then SD will learn she won't get rewarded and she can't treat BM that way.

Good luck...

In a perfect world, I think both Dad and Mom need to be on the same playing field. It is in the best interest of the child to know that her parents are united in raising her. What is unacceptable at one house should not be at the other. Also, the child probably knows that Dad knows of her bad behavior at Moms and can get away with it at this point. With that said, there are just some situations where that is not at all possible.

We had the same problem for years, to the point where BM would actually call me, the SM, to talk to SD when she was acting up. She kept asking what we would do to deal with SD's tantrums and fits and we kept telling her 'she doesn't do that here!'
You really can't change BM's behavior, so the best you can do is try to work with her. If there is any chance of getting you all to sit down and set some guidelines that are followed at both houses so SD has consistency that would be ideal. Things like 'no screaming in the house. You will be given one warning, and then the next time it's 3 minutes in time out.' But both homes have to follow this and be consistent for it to work.
The other thing you can do is when you offer praise; offer it from the three of you. "Mommy, daddy and I are so happy when you don't scream in the house. Doesn't it feel good to have Mommy, Daddy and I proud of you?" or "You know Mommy, Daddy and I don't allow you to run into the street. You need to hold Mommy, Daddy or I's hand when we are in a parking lot." If you lump her in SD may pick up on it and change her behavior without really thinking about it. We would do that often and it did have a positive effect . . . until SD got older and figured out how to use our differences to her advantage, but we'll save those stories for another day!!