I too am a step mom of two boys 7 & 9. I do discipline them on rare occasions that they act up and my husband happens to not be there or know what happened. However, my husband and I agree on what disciplinary action to take and what actions deserve discipline. when they argue we have a job jar, they must complete the job together without fighting or they do another, if one hits the other that one goes to their room (we have a strict no physical contact rule), if they lie they go to their room, other than that they've yet to do anything that really warrants disciplinary action. Now we only have to threaten the job jar when they argue, they will work it out on their own or come to us. If they argue over a toy we take it away.
You just have to first sit with your husband when the child is not around and lay down the rules for her together and the consequences for breaking the rules. as it has previously been said, the child is in your house and you and your husband are in a partnership, therefore your house your rules. Your husband wouldn't take his child to a friend’s house and allow her to be disrespectful or break the rules of their house their right? (I.e. taking shoes off at the entrance) so it makes sense that she should respect you and your house rules as well. The child will learn the rules just like my stepsons did. At their moms house she allows them to hit, or that's what the boys have said, but in our house we allow absolutely no violent physical contact and they know this. Children have different rules when they’re at school, library, playgrounds, friends houses, etc, she'll learn your rules as well, but you and dad have to be on the same page. Don’t just take things into your hands.
Now as for the living with you thing, I have to agree with dcroberts on this. You married her father, therefore where ever her father is that is HER HOME. I've repeatedly told the boys that their father’s and my house is their home and always will be. They are always welcome there no matter what and should they decide to live with us that's fine. That child will come to resent you if you do not let her feel at home. That child and my stepsons and any other stepchildren need to feel loved and wanted, even if deep down you don't feel that way yet. I know that I've always cared for my stepsons and gotten along with them very well, but loving them as my own, that's hard to do especially if you don't yet have your own yet. Loving your own children is easy. It’s unconditional and comes naturally. You get to experience them developing their own personalities and to an extent help mold them. Loving stepchildren and having a good relationship with them is hard, much harder than having your own. That relationship requires a lot of work on both parts, you have to build trust, you have to get to know their personalities and work with it. That sort of love doesn’t come naturally. I’ll tell you what though, after having my own child our relationship has changed. It’s become a lot easier. Before my child I was hesitant to show them any physical affection, like hugs, because they weren’t mine. I didn’t want to cross any boundaries. But having your own child I think helps to transcend any boundaries that once existed.
Mother is the name for God in the lips and hearts of little children. ~William Makepeace Thackeray