Child care expenses incurred when a parent is working are an "add-on" expense, meaning that like medical expenses, it's separate from "basic" support, and the parents will share the expense in proportion to their incomes. However, in certain case, parents may choose that they will each pay whatever child care expenses they incur.
Note that summer camp is a child-care expense and the expense is divided between the parents pro rata, unless they agree otherwise.
Does the day-care count as child care? Nanny?
Day care definitely counts as a child care expenses. A nanny will likely count, assuming the expense is reasonable and is for a period of time that the caretaking parent is working.
Can I pay my mom/dad/other relative for taking care of the child(ren)?
Yes, assuming that the alternative is that you would have to pay someone else to watch your child. Note that the expense must actually be paid, however; you can't make up a fee and then collect from your ex, without actually paying your relative. Best practice is to agree on the financial aspect of it in writing, and to get receipts. It may seem silly to get a written invoice or receipt from your parent or relative, but if you're looking to classify this as reimbursable child care, that's what you need to do.
Does summer camp count as child care?
It depends on the circumstances: the cost of the camp, the other alternatives, and both parties' financial circumstances, to name a few. Best practice is to address summer camp specifically in your settlement agreement.
Does this mean I get to charge my ex for half of the cost of the babysitter?
No. Child-care expenses are shared only when they are incurred due to one parent working, or seeking work. This means that the non-custodial parent is rarely in a position where he (or she) would incur reimbursable child-care expenses.
What about a situation where I have to go out of town for work, my ex is not available to take them, and I arrange for a relative to take care of the children?
You should address this specific situation in your settlement. You may give the other parent a "right of first refusal." If he (or she) declines to take the children while you are out of town, then you would be entitled to pay a friend or relative a reasonable amount for caring for them and to share that cost.
What about summer camp?
The cost is divided in proportion to your incomes. You may seek to have the amount limited so that you are not stuck writing a blank check for an expensive camp.
What if I don't agree that the children should go to summer camp?
This is a legal custody decision, so it would be decided based on that aspect of your agreement. Some of the issues that seem to come up over and over are:
1) Parents disagree on at what age a child is ready to go to sleep-away camp. The answer is that each child is different, and if the parents can't agree, then the judge will probably interview the child and then decide.
2) One parent wants to send the child to Asphalt Green and the other parents says it's too expensive. The answer is that, again, if you can't agree then the court will make a decision for you. If you are the parent resisting AG (or a similar camp) on the basis of cost, it would probably be a good idea to come up with a few concrete examples of less-expensive camps that would work for you.
None of this is to imply that kids need to spend their entire summer in camps. The judges are aware that kids' having a little down-time now and then is fine, too.