Deductions & credits

To address part of your original question:

"... the amount he 'contributes' wouldn't even cover rent, let alone all the other expenses that goes into taking care of our child. So how is it that it was determined that he is contributing more than I am? Can I report this to the IRS?...?

The IRS - No.   That is a question that you should have asked when the divorce decree was being negotiated.   If you think the terms are incorrect or circumstances have changed then you should  consult your divorce attorney that wrote the agreement and the court that issued it to possible modify it.   Neither the IRS or anyone else can help with your divorce decree.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**