Good news, I just tried the one combination I had not yet tried, and it worked.  I enter the child's information in the Dependent Section, indicating child lived more than 6 months with mother.  I made the Qualfied child/dep care code Q (not a dependent but is a qualifying person for earned income credit and/or the credit for child and dependent care expenses).  I entered name and social security number in Part II Federal Filing Status for Head of Household.  This question has been answered!