Its not an easy answer without all the facts.  You'll need to go through the rules for Head of Household and see who qualifies to claim the baby. See Pub 501, Page 8-9- lots of examples:

https://www.irs.gov/pub/irs-pdf/p501.pdf 

Also note that Head of Household status is now included on the 8867 Preparer Due Diligence Checklist:

https://accountants-community.intuit.com/articles/1670953-form-8867-preparer-s-due-diligence-checkli...

House deductions can be split however best suits them.

Also, some CPE or Educational books include an HOH flowchart type worksheet...I get The Tax Book for Federal and Small Business and Trusts, and Spidells  Big Blue Answer book for CA each year.