You and your GF are confused about some things. GF cannot file as HOH unless she has a qualified dependent. GF needs to file Single. Since you are the higher earner, you can file as HOH ---and you say you are claiming the children.
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.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
