Why are there some people on here insisting that this is DSD's home? It isn't.
I am a step-daughter. And I am also a stepmother. And my DDs have a stepmother. In all these scenarios, the step-children's actual home is where they live, with their mother. Their DF's and SM's home is where they go and stay, and where they hopefully feel welcome and 'at home'.
We used to go and stay with our DF and DSM, but we actually lived with our mother, so that was home. My DDs would go and stay with their dad and step-mum, but their home was where they lived, with me. My DSCs would come and stay with us, but then they would go home to where they lived with their mum. So what is it that makes some people so insistent that OP's home is her DSD's home?
OP, you and your Dh need to come to agreements about what is and isn't acceptable behaviour from all your children. They all need to know that you are together on how things work in your household, and your DH needs to not be afraid to actually be a father to his daughter by giving her boundaries and helping her to grow up into a decent person. Obviously, he cannot be responsible for how his ex chooses to behave. But he can say what he will and won't put up with as a parent. And he needs to. It is part of effective parenting. There need to be consequences for anyone overstepping those boundaries.
I don't think banning her from your house is the solution. This behaviour needs to be dealt with, regardless of what DSD's mother has to say about it. It is not for her to say what goes on in your household, only you and your DH make those decisions. If DSD doesn't like the consequences of her behaviour and strops off for a bit, then fine.
It is unhealthy for children and teenagers to think they can dictate and manipulate within the family to get what they want. This lack of respect within the household is unacceptable, and it will feel safer for all the children, even for your DSD, if they understand that the adults are actually in charge, not the kids.
If you and Dh don't see eye to eye on how to deal with DSD's (or any of the children's) behaviour, then you could always go together and get some CBT to help you sort this.