i have searched far and wide, but still baffled with this

Scenario:Father and mother divorced from each other in 02, got back together and been living together with 2 children...

Father makes most $ wants to claim HOH, but NOT claim 2 kids as dependents on his return. Mother makes less, so she wants to file single and claim both kids as dep since she qualifies for EIC.

Can this be done? If so, In the HOH box on 1040 form, would he reference one of the children since only one blank?