Neither "taxpayer"'s GF or her grandchild can be qualified dependent for Head of Household because neither of them is related to the taxpayer. They might be dependents for the $500 credit for other dependents, but that is all. No Head of Household filing status, no earned income credit, no childcare credit, no child tax credit for the grandchild who is not biologically related to the taxpayer.
Sorry---You cannot override tax laws.
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