I suggest that there is not much your husband can do at this point. He has visitation twice monthly. For how long? Unless she spends a couple of weeks with him each month, he has no workable way to now begin making and enforcing rules that will make a major change in the way she deals with life. It's too late to change her. But not too late to make life more bearable while she's in your home.
Are any of these children living with you? If not, I suggest that all of the kids are angry with their father for not having taken charge early in their lives and thus resent it when he tries to do so now. I encourage him to find a way of setting boundaries and giving natural consequences for them while they are in your home. Give consequences that do not require co-operation from her mother.
I do urge you to encourage him to be forceful in insisting that everyone be respectful of everyone at all times. Have a family meeting and talk about what respect involves, how we show respect, what counts as disrespect. Then.....tell them that there will be an immediate consequence for disrespectful behavior. In the restaurant situation, I suggest that the immediate consequence is that he drives her home. The rest of you finish dinner. He can come back to get you later. If you're at home, the immediate consequence is that she goes to her room and stays until she can come out and apologize for being disrespectful.
This will not be easy to enforce. You will have minutes, perhaps many minutes of a stare down. All action stops until she's in her room. He cannot physically force her to go to her room but he can make it uncomfortable enough that she will go.
The family meeting is most important in making this work. The siblings need to understand what is happening and stay out of it. And....if they're disrespectful they need to have the same consequence.
I say immediately because you know from experience that there is no way to stop her once she gets going. She is being unreasonable and needs to be stopped. The rest of the family deserves to be treated better than this. Why do her siblings think he's treating her unfairly? This needs to be discussed with them so that they understand the importance of respect.
Focus only the the issue of respect for now. Once she understands and is able to be respectful you might choose to talk with her about how dressing the way she does and posting the pictures she does is being disrespectful of herself and her body.
Are the other children, for the most part respectful? The brother that she attacked: did he think it was alright for her to talk with him that way? Why are they protective of her. Is she the only one having obvious difficulty? Perhaps the other children are step-siblings or live with you and she's the only one who visits?
I urge you to get family counseling. Start out with counseling for you and your husband so that you can support each other and build up your confidence in what must be done.
Because she doesn't live with you, I wouldn't expect that taking away things or privileges would be effective. As you said her mother can countermand the discipline. It sounds like her mother and father are not able to talk with each other and co-operate in managing their daughter's behavior. If that is the case, whatever your husband does must be something that she cannot undo.
He can stop paying for her phone service. Since her mother bought her new service, I recommend that he permanently end the service. This is an immediate consequence for the mother. Yes, we all, even adults, have consequences. I suggest that by permanently canceling the service he is letting his daughter know that he does follow thru on consequences and he's letting the mother know that even tho she doesn't back him and his discipline he will still discipline.
Because your husband has difficulty being firm, I urge you to take a parenting class with him. I also urge you to get and read the book Disciplining with Love and Logic by Foster Cline and .......
Surely, he has an incentive to change the way he treats her. We do usually have to get angry to change the way we handle things. Give him a lot of praise for what he did. Accept for now the anger that it takes for him to discipline. Once he becomes comfortable with the idea that taking a stand and requiring respect he will be able to do so with less anger.
He, as with lots of us, have the mistaken idea that if we just let things go that we can have peace. He's learning, the hard way, that ignoring his children's behavior does not create peace. Only having definite boundaries and consequences for when they're crossed creates peace. He's way behind with his daughter. Finding peace will take a long time but it will be worth it and is absolutely necessary for his daughter's and the whole family's welfare.
Julie L, I was ready to send a flower until I read your last sentence. Who is not at fault here? And what do you mean by fault. The mother, father, daughter are all responsible for their own actions. It is the parent's responsibility to teach their children to be respectful. I do not blame anyone but I do insist that everyone takes responsibility for what they did or did not do. It's only be accepting responsibility that we can see that we need to change what we're doing once we realize that what we have done was not effective. Placing blame, in my opinion, is not helpful. It only makes people feel guilty which then makes it more difficult for them to be productive. In this case both the birth mother and father as well as the daughter are at "fault."