Q. Can I file as Head of Household (hoH) under these circumstances?
A. No. For HoH filing status, you relative must live with you for more than half the year*. That requirement is in addition to the requirements to be a "Qualifying Relative " dependent.
Why isn't the person(s) she lives with claiming her as a dependent, instead of you. She only qualifies you for the (up to) $500 other dependent credit. But should would qualify a relative she lives with (most likely) for the (up to) $2000 child tax credit and maybe some Earned Income Credit.
*There is an exception if the relative is your parent.