Unmarried parents living together with 3 children. Father gross around 70k, mother gross around 24k.

Unmarried parents living together with 3 children. Father gross around 70k, mother gross around 24k. Looking for max refund however kids must be split up

One child is stepson, mother signs Form 8332 so child's father that lives elsewhere can claim as a dependent, mother wants the EIC.

Of remaining two children, can Father claim 1, and all deductions, credits and benefits, and mother claim the other for all deductions, credits and benefits? Should Father (head of household) claim no children and let mother, since mother claiming would equal refund of almost double what father would owe, without claiming dependents?