I think in US, they normally won't split kids between parents.

Especially your kids are very young. Are you sure that your mood is not affected by hormone? A very outgoing friend of mine was kind of "depressed" for quite a few months after giving birth to her child. You may want to talk to your OB and have her recommend some specialist for you. Have you tried marriage consoling? Also, you may separate for a while. You live with both your kids.