You don't say where the kids live. Just because you're the parent doesn't mean you're entitled to claim them. There is a limit to how much child tax credit (and earned income credit) you can get. It is not a straight $2000 per kid.
The money you hear about people getting for just filing a tax return claiming kids requires them to have some earned income (wages or self employment). Without earned income, they are not eligible for the "refundable" Earned Income Credit or Additional Child Tax Credit. Both credits are calculated on the amount of earned income you have. No earned income means no "refund". A small amount of earned income means a small refund. The child tax credit does not "kick in" unless you have at least $2500 of earned income.
A child can be the “qualifying child” dependent of any close relative in the household. If you live with someone else, e.g. your mother and sister, it may actually be better if they claim your child(ren).
