Hi Lovelight,
Welcome to the site! Your post wasn't long at all. I can match your long post and raise you a few paragraphs

Step parenting is hard Even mild/moderate BPD can be difficult (starting the divorce in 2009 and finishing it in 2015 makes me wonder if the BPD is more on the moderate/maybe more-than-moderate side).
My challenge is that the work and bonds we create are undone when the kids go to their BPD mom, due to misinformation "mom says... ." or what they say are their own negative interpretations (about money, our relationship, our feelings for them, the list goes on). Initially the kids were warming up to me, but since we moved in together there have been a lot of false accusations about me such as: getting in the way of them spending time with their dad, take their money, meeting him before they were separated etc. There is also a general climate of disrespect modeling their mom's anger and disrespect toward their dad and now me.
There are two really good books recommended here a lot. Divorce Poison by Richard Warshak is pretty much the classic. You're experiencing parental alienation tactics, and that requires a very specific type of response that is different than the norm. We want to avoid putting the kids in the middle, but a BPD ex cannot do that. So with the kids already in the middle, you have to adapt your response. There are some other really good resources in Lesson 6 to the right ---------->
I would also go through Lesson 5 on raising resilient kids. There are specific techniques to help manage these interactions that can be very effective, especially validation. It takes some practice -- I'm still learning. It seems to change a bit as the kids get older (my son is 13 and some of his reactions are challenging) but they tend to become the things that really count when there is one severely invalidating parent (BPD) and the other who is very validating (you and your stb H).
Another thing (new for me) is reading about the normal emotions of kids and divorce. Some of their reactions are likely to be BPD, but the kids are also struggling with plain ol' stress from having their parents split. I got a lot about of this article on
Typical Reactions of Kids to Divorce.The reason I mention that is because they are probably coping with stress in typical ways, but they have a BPD mom who sort of fuels it for them. Seeing that might help you separate out what is their stuff, and what is hers.
My son is rejecting my SO pretty hard core right now. S13 says the same thing you mention, "He tries too hard." Except SO is just being himself. He has 3 teens and this isn't his first rodeo and he's not trying to knock himself out because he knows how these things go. Apparently saying "hi" to S13 is "trying too hard." My T said to try reverse psychology, and that has had some effect. For example, S13 will say he doesn't like SO, and I'll say, "Ok. I understand. You don't have to like him." Then I move on like it's no big thing. Because honestly, it isn't. I wish S13 did like SO, but it's also not going to change what I do if he rejects him.
Anyway, welcome to the circus.

You're in a good place with people who understand.
LnL