Domestic Partner's child

I am in a registered domestic partnership & my partner has 4 children.  She will be claiming 3 & I will claim 1 as my stepchild.  We each paid some day care expenses.  So, do we both get a Child Tax Credit?  Also, when it asks who did the child live with, would the answer be me, or both parents the same amount?  I also have my own child & per divorce & have authority to claim that child as my dependent.