Deductions & credits

You need to carefully follow the interview.  
Yes, you care for a child. 
Yes, the child lives with you more than half the year (or choose all year). 
The other parent will claim the child for the credit.  
You will give the other parent a signed form 8332.   

That should create a situation where the child is not your dependent but is qualified for head of household status, EIC, and the child care credit.