If a married couple has 4 children, can they file separately and each parent claim 2 children? Or one parent claims 3 and the other claims 1?

If the father gets a 1099 (earns approx. $40k) at the end of the year and the mother earns less than $20k (gets a W-2) for the year, could he file separately as head of household and claim 1 or 2 kids of the 4 and then the mother files separately and claim 2 or 3 kids?