You cannot do that.
The child can only be on one return - the credits cannot be split.
Qualifying Child of More Than One Person
Sometimes, a child meets the relationship, age, residency, support, and joint return tests to be a qualifying child of more than one person. Although the child is a qualifying child of each of these persons, only one person can actually treat the child as a qualifying child to take all of the following tax benefits (provided the person is eligible for each benefit).
1) The exemption for the child.
2) The child tax credit.
3) Head of household filing status.
4) The credit for child and dependent care expenses.
5) The exclusion from income for dependent care benefits.
6)The earned income credit.
The other person can’t take any of these benefits based on this qualifying child. In other words, you and the other person can’t agree to divide these benefits between you. The other person can’t take any of these tax benefits for a child unless he or she has a different qualifying child.