G.,
I dont know her mom but if you and she have any kind of relationship it would be good for all three of you parents to sit down and come up with a consistant plan that you will implement in both homes. Children strongly need structure,discipline and security. If there home life is vastly different with there mom it may be very hard for yourself and your husband to correct this behavior. The only thing you can do in that case not haveing her Moms support is show her a different example in your home and pray for the best. You can your husband could implement a plan ie...rules,punishment,and if behavior is better a reward system and together communicate it to her clearly.Keep it short. They are teenagers after all and attention spans seem to be short.I have a 13 yr old and she would lie to us about the least little thing. We made the rule...if you tell the truth the first time there is no punishment at all for most anything,if you lie and continue to lie the punishment progresses with the lie. If you can work it out with her mom then she should be grounded at both homes if she gets grounded at one.When my daughter gets grounded it means she has to stay in her room. She can read and that is it. No electronics of any kind and if we had family plans, well she ruined it for herself. She gets to stay home with a baby sitter.(Not even out to dinner with us) It may sound harsh but I am more interested in raising a child who will make good choices in the future based on knowing the consequences could be harsh. You are correct she is not your friend and is unable to handle an adult relationship. There is plenty of time to be friends with our children after they are adults and can handle it.
You may also want to find out who her friends are. Offer her a sleep over at your home if you live close. Sometimes the friends they keep are a good indicator of why things are happening. If her mom works full time she is probably not as vigilant as she could be. Understand I do not know the whole situation and am not judging you. I am just hopeing something I say will strike a cord and help.
Children equate love with letting them do whatever they want. When they grow up they usually if they have any moral compass at all, tend to resent the parent who wasn't consistant. They realize that discipline and control is the biggest form of love.
I was a lieing,out of control teenager. I was molested as a young girl and struggled with alot of issues. One of which was lieing. I was taught to lie by haveing to keep the biggest lie ever a secret. God saved me. I was 12 when I told my parents and they did nothing. I dont blame them because, I dont thing they knew what to do. Afterall, I had been a liar my whole life.
So, now that you know I have a little insight I can only tell you if those things do not work, try talking to someone she looks up to and respect to talk to her. If you are in a church,or any social circle encourage friendships, relationships with children you know are more in line with your ideals for raising her. Then help those relationships to grow by planning things with that child to be with your daughter.
Lastly be a strong influence in her school. The more you know the less she can lie about. It will also help develope a strong relationship. I am sure she is still struggling from the broken home thing. No little girl ever wants to be without there dad. You will find that whatever you do she will love you for trying once she is older and has kids of her own. Goodluck and pray alot.