Each child can only be claimed once, the parents must decide which one claims each child.
So, if you have multiple children each parent can claim a child or one person can claim all but the total number of dependent children claimed on both returns can not be more than the total children in your household.
Also since you are both living together only one of you can claim head of household.
Please see the link below for more information.
https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...
