One thing you need to remember is whichever one of you claims the child, they would claim all tax attributes. One person has to claim all of the tax attributes if you live together, as the child would be a qualifying child of both of you.
From Publication 17: "Sometimes a child meets the rules to be a qualifying child of more than one person. However, only one person can treat that child as a qualifying child and claim the EIC using that child. The paragraphs that follow will help you decide who, if anyone, can claim the EIC when more than one person has the same qualifying child.
You can choose which person will claim the EIC. If you and someone else have the same qualifying child, you and the other person(s) can decide which of you, if otherwise eligible, will take all of the following tax benefits based on the qualifying child.
- The exemption for the child.
- The child tax credit.
- Head of household filing status.
- The credit for child and dependent care expenses.
- The exclusion for dependent care benefits.
- The EIC."
If you are claiming them as dependents, only you can claim them for any tax benefits, including Head of Household and day care credit. The father may NOT claim them for EIC.
You may have heard of a special rule in the case of divorced & separated (including never married) parents. You are not eligible for this treatment. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.
This is because he is answering the interview questions as if he is the custodial parent allowing the non-custodial parent to claim the dependent. Since the interview can be confusing, the simplest thing to do is not enter his children in the dependent section.