Can I request that she pays the new attorney fees that I will incur?

In February of this year, my ex wife and I went to court for custody of our children. (This is my wife'ss yahoo account by the way.) We received 50/50 shared custody and she was denied the right to move out of state. Not even a year later she is trying to move out of state again and take the kids when it is not her time. I was informed by the attorney that I would have to pay court fees and attorney fees all over again and this just seems stupid and costly when we already have a judgement and we will go in front of the same judge again. My attorney won't be back from a seminar for another week and I am planning on asking him if I can charge the new attorney fees to her since we already have a judgement less than a year old. He stated before he left that we would start with a certified letter and see if she agrees to the proposition, but she's still refusing. He did say we could hold her in contempt of court for keeping the kids away and it could end up in jail time, but that it looked like we'd end up back in court again. I have followed every rule I was supposed to and I am just wondering if anyone would know or could tell me from personal experience if attorney fees could be done like that?