You cannot claim head of Household unless you are claiming at least one dependent. You are also not HoH because you lived in somebody else's home for more than half the year. But you do not need to claim HoH, as you income tax will be zero whether you use HoH or single status. You will owe some self employment tax (social security and medicare); about $730.
Either you or your daughter my claim your kids. Under the rules, the are the qualifying children of both of you. You may choose who will claim them or you can each claim one. But you cannot both claim the same child. Since you are allowed a choice, you should do test returns to see which way the family comes out best. Try this tool <a rel="nofollow" target="_blank" href="
https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1">https://turbotax.intuit.com/tax-to...>. Enter
If you cannot agree on who will claim them; you, as parent, have first choice. The fact that you have not paid housing costs while living with her, is not relevant to the IRS.
Reminder: your daughter cannot claim you. You do not qualify as her dependent.
