Legal Question in Family Law in California

File and serve a petition for paternity with a motion to establish custody and visitation.

You would need to file a paternity petition so that you can have a judge order custody and visitation orders. I don't think the schedule you suggest (if I understand it) is appropriate for a 10 month old. Babies that young should not go extensive periods without either parent. California courts have a website, and the L.A. Courts have a pamphlet suggesting an age-appropriate parenting plan:

http://www.courts.ca.gov/selfhelp-custody.htm

scroll down to the bottom and look under the heading "more information on parenting your young children" and click on the pdf that says "creating a parenting plan:children under 3". Maybe you two can figure out a way to move out on your own so that your baby doesn't have to grow up in two homes? Good luck to you.