The money you hear about people getting for just filing a tax return, claiming kids, is dependent on you having some earned income (wages or self employment). Without earned income, you are not eligible for the "refundable" Earned Income Credit (EIC) or Additional Child Tax Credit.
In your situation, it is usually better if some other relative, in the household, claims the kids. Alternatively, the non-custodial parent could claim them, as dependents, and the child tax credit, but not the earned income credit. Only a relative the child resides with can claim the EIC, based on the child.
