If he is court ordered to pay those extras (and childcare is an extra that will be put in arrears if he isn't paying), then file contempt of court charges compelling him to pay. If it is just a verbal agreement, then there is nothing you can do about the past.
But you can file for a modification of child support and ask that childcare is added on to it. You will need to provide proof of your actual cost.
You probably aren't going to be able to get the tax exemptions changed unless he is in arrears on his financial obligations to the child.
Unless you have a right of first refusal, there isn't much you can do about his taking the child to his parents.