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@bob808 wrote:
 But if the higher income taxpayer claim claim head of household and the lower income taxpayer can claim both dependents

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That is not allowed.  Most likely, these are your options (assuming both parents agree):

Option #1: Parent 1 claims Head of Household and two dependents.  Parent 2 claims Single with no dependents.

Option #2: Parent 1 claims Head of Household and one dependent.  Parent 2 claims Single with one dependent.

Option #3:  Parent 1 claims Single and no dependents.  Parent 2 claims Single with two dependents.