if my daughters father claimed her can I still get the child tax credit but not the EIC

Are you the custodial parent?  Do you have an agreement with the other parent to allow the other parent to claim them--due to divorce or that you live apart and share custody?  Did one of you sign a Form 8332?

If there is a signed 8332 then the custodial parent retains the right to file as Head of Household, get earned income credit and the childcare credit.  The non-custodial parent gets the child tax credit for children under the age of 17.  If the child is 17 or older the non-custodial parent gets the $500 credit for other dependents.

If you and the other parent have a signed agreement, you need to indicate in MY INFO that you have such an agreement.

As far as the IRS is concerned, the custodial parent is the one with whom the child spent the most nights during the tax year--at least 183 nights.

If you are a non-married couple who live together with your child, then only one of you can claim the child(ren) and the one not claiming the child does not enter anything at all on their tax return about the child.   The “sharing” of child-related credits you may have heard about is only possible between divorced or never married parents who live apart and share custody and who have a written agreement to share the credits.    The child’s SSN can only be entered on one tax return.   Any other return with the child’s SSN on it will be rejected.   If you are a family, then work out how to share the refund between yourselves.