@rickwm
You have to make a distinction between the rules for filing as head of household and the rules for claiming a child as a dependent.
The requirement for filing as head of household is that you pay "more than half the cost of keeping up a home." The cost of keeping up a home is not the same as providing support for a dependent. Here's how IRS Publication 501 (page 😎 defines the cost of keeping up a home.
Costs you include. Include in the cost of keeping up a home expenses such as rent, mortgage interest, real estate taxes, insurance on the home, repairs, utilities, and food eaten in the home.
Costs you don't include. Don't include the cost of clothing, education, medical treatment, vacations, life insurance, or transportation. Also don't include the value of your services or those of a member of your household.
So, for example, clothing for a child is part of the child's support, but it is not part of the cost of keeping up the home. "The expenses of their separate children" does not affect the cost of keeping up the home.
It is never possible for two people living in the same home to both file as head of household because only one of them can pay more than half the cost of keeping up the home.
