Also, my wife is petitioning so that only she can claim our son as a dependent. However, she is also wanting me to pay 50% of the child care costs. Can she do this? Will I be able to claim any dependent care on my taxes?
If she is the custodial parent, she gets the exemption per the IRS unless there is a court order stating differently or she signs a form saying you can have the exemption. Courts typically split the exemption with 2 or more kids or alternate it.
As for the dependent care, that all depends on how your child support is calculated. When mine was calculated (I am the custodial parent), the tax benefit was included in the split. Which means that he isn't paying a true proportional percentage of childcare. As a result, I get the childcare deductions.
A CPA who does taxes would be better able to answer this question.