My husband has three step daughters all four years apart.
I don't know.
I do know that it sounds like she feels she needs more attention than she is getting. Have you tried giving her mainly positive attention and while not ignoring the bad behavior but giving it little reaction. Implement the consequence but don't engage. Don't get into a discussion about why she lost her tv time if she hasn't done her homework. She made a choice to do (or not do) something so she made the choice to accept the consequence. It is her choice. If she does good and what she is suppose to then she gets more attention. Maybe she can work towards one-on-one time with you or her dad?
I don't know your step daughter so I don't know if you or your dh handled it the right way. Some people will say anything, even things they don't believe or have any intentions of doing to get a reaction and hopefully get out of doing something they don't want to. It sounds to me like she didn't want to go to her mom's. Her behavior at her mom's is reinforcing that for me. This type of behavior is also a way to deflect an argument from what you did to how unfair the other person is being. It becomes about the attitude rather than the fact that I got my ears pierced. If I get my mom yelling about the fact that I'm being rude then I don't have to admit that I should have asked before I went and got my ears pierced.