the W-4 is just a way of adjusting your tax withholdings so that it minimizes what you owe / get refunded on April 15. it should have nothing to do with whether your daughter (or your other children) are eligible for health care under your employer's medical plan
I think the broader question is whether two people who live under the same roof. but are not married can each claim head of household.... please be sure to run your situation and your fiance's situation through the IRS assessment tool:
https://www.irs.gov/help/ita/what-is-my-filing-status
one of the questions in the tool is whether you provided more than half of the cost keeping up a home in which you lived...and you both can't answer 'yes' since only 1 person can provide more than half the cost of keeping up the home.
