Maybe I'm alot more stubborn and bull headed (hubby says I am) but when we had his daughter living here for 3 months (her mom dumped her off without warning and had no contact for the entire time) I had a similar problem with hubby. Thankfully his daughter was never violent but hubby would never do what was right in correcting her from her badmouthing, and not obeying simple rules.

I figure I married him, so she's MY step daughter and I should have a part in her raising when she's living in MY house! I took the initiative and took care of business. Since hubby didn't want to deal with the situation anyways he grumbled to me a bit about my tactics but let me do what needed doing.

Had she have been violent to the point of knocking someone out then I'd be on the phone to the police and maybe a couple hours in a jail cell would chill her butt out and make her realize that actions have consequences.

That's just me though, I don't know that everyone could/would react the same way in similar circumstances.