Very, very, very difficult thing to deal with. What sort of counseling did you go to? A family therapist? It didn't work I presume? You can always go to another therapist. The relationship you have with a family therapist has to flow easily. If it doesn't, you might as well be talking to a brick wall. Make sure you choose the right therapist for your family.
I can't and I don't think anyone on here could explain to you word for word on what exactly to do in this situation, but I'll make some suggestions if I may and you do what you please with them.
This is a matter of two, and in some cases three separate households if you count your children, coming together and trying to be the same household every other weekend (or whenever your husband gets his children and you get yours). Even if his children's mother was not lazy, it is doubtful that she would share the same parenting philosphies that you do. There is always going to be some friction. It is a good idea to accept that and focus more on how to deal with the friction when it comes.
Most of how this situation will be dealt with depends on how willing your husband is to stop babying his children. If he's not willing to then you should decide if you want to make a battle out of this. I would not choose to make a battle out of this. It is his child. He is responsible partly (his ex-wife the other part) for how he provides her with the skills to become a productive adult. You, as her stepmother have a role as well but not near as huge as her father does. Your husband might not respect your opinions or advice on how to raise children since yours chose to leave and live elsewhere. This may not be the case, but it could be. Will he ever tell you that? Maybe, maybe not.
If you want my advice, let your husband bear the brunt of this one...for now. Be there if you are needed by your husband and his children. For right now, let them work on this within their own circle. I'm thinking this 9 yr old is acting like this for exactly what she is getting, the extra attention. As long as your husband allows it, she'll continue. It's up to your husband when this stops. It isn't up to you or the nine year old. It won't matter how much you nag him or make suggestions.
I want you to understand why I'm asking that you keep your distance. It is bc most children put up a brick wall between themselves and "intruders." You are probably considered an intruder. You can't take the wall down. It is up to the child to let it come down. It will, gradually and it will depend on how you act as well.
I hope this helps. It's so hard to give advice for complex situations on a computer screen. Don't stress, stressing only makes it worse. Sometimes it is best to let things alone and not make a huge deal out of them...then they tend to fade on their own if they are allowed to.
Wo ist das kamerahhhhhhhhhhh!!!