I have an 11yr old defiant daughter. This has been going on for about 2 years. She continually lies to our faces, to her teachers and her friends. She has forged my name on school work, until the teacher finally caught on. She has stolen another student's shirt from school that was for a project because she did not like her shirt. She doesn't do certain school work. And many times lies about doing it. She will not do the one and only chore she has at home (feed dog). When she is grounded she goes behind our back to do the things she shouldn't be doing. Or she continues to do the things that got her grounded in the first place. We have a reward system in place. But no sooner does she earn the reward, she loses it. She cannot explain why she does not do what she is suppose to do. We have had many discussions. I am at my ropes end.
Kids often act out their emotional upsets and are unable to use words to explain what is bothering them. Often they do not even know exactly what the issue is underneath their acting out behaviors. However, you can be fairly sure that unacceptable behavior is a sign of something emotionally stressful going on under the surface.
One thing you can consider is making sure that your home routines are consistent and predictable, that there is no adult conflict happening in front or the child/children or within earshot, and when you make rules and consequences, stick to them.
If these measures are unsuccessful, you may need to invest in professional help for your daughter or even for the family, to determine what is at the root of these issues and to correct the behavior.