If my daughters father gets to claim her this year, do I still claim head of household, EIC, or child care? He only gets her every other weekend?

Yes, you can still claim these benefits. In the case of divorced parents, the non-custodial parent can claim the dependent exemption and the child tax credit with a court order or agreement but only the custodial parent can claim the head of household filing status, the credit for child and dependent care expenses, the exclusion for dependent care benefits, the earned income credit, or the health coverage tax credit. Generally, the custodial parent is the parent with whom the child lived for the greater number of nights during the year

The custodial parent must use either Form 8332 or a similar statement (containing the same information required by the form) to make the written declaration to release the exemption to the noncustodial parent. The noncustodial parent must attach a copy of the form or statement to his or her tax return. This can be found in TurboTax under the Federal Taxes Tab (Personal in Home and Business) --> Other Tax Situations --> Miscellaneous Forms --> Release or Revocation of Release of Claim of Exemption for Child.