First, head of household is determined by physical custody during the tax year - not the divorce decree. Your ex-husband can only use one of your son's for head of household filing status if your son slept in his home for 183 (184 days in a leap year) days of the year. If both of the son's lived with you for the majority of the year, you are the only one that can claim the children for head of household filing status.
If there is a son than lived with the other parent for more than half of the year that you can claim as a dependent, you will need to make sure that you indicate that the child lived with you for less than 6 months of the year, there is a custody agreement, and that the other parent is letting you claim your child as a dependent.
Tax benefits for children are split as follows when the custodial parent allows the noncustodial parent to claim the children as dependents:
The parent that had physical custody gets:
- Earned income credit
- Child care credit
- head of household filing status
The noncustodial parent gets:
- Dependent exemption
- Child tax credit.
