Yes---try it both ways to see which is better. What you CANNOT do is file a joint tax return if you are not legally married. And each child can only be on ONE tax return--so decide which parent claims one or both children. There is no "sharing" of the child-related credits if you are all living together as a family. The one who earns the most and pays over half the household expenses is the one who can file as head of household.
If you somehow do not agree on who will claim the children, there are tie-breaker rules:
TIE BREAKER RULES
https://itap1.for.irs.gov/owda/0/resource/Commentary_Files_Redirect_ITA/en-US/help/tbrk09.html
**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.**
