Can a parent recover child support if they don't have custody?

My ex husband gave me full custody of our child due to a domestic violence incident back in January of 09. He only wanted to see the kids 2 weeks of the calendar year. In September of that year I allowed my daughter, then 15 years old to reside with her father for the school year. He is a physician and was ordered to pay child support all along, however I waived his child support during the time he had with our daughter only to be fair.

He is now asking for back child support.

My daughter resided with me again exclusively for the summer of 2010.

Does anyone know any court case related to this?