Only the custodial parent can claim child care expenses. Here's how the IRS defines the custodial parent (in IRS Publication 503).
"The custodial parent is the parent with whom the child lived for the greater number of nights in 2016. If the child was with each parent for an equal number of nights, the custodial parent is the parent with the higher adjusted gross income."
There can only be one custodial parent for each child. You cannot both claim child care expenses for the same child.
It doesn't matter whether your separation agreement defines custody differently. The IRS definition applies for tax purposes.
