because they did not live with you, your son and the grandchildren are not "qualifying children" (the $2000 tax credit), but they are "qualifying dependents" (the $500 tax credit). I assume they are US citizens and have SS numbers.....
As the name implies, the earned income credit is a credit against EARNED income. Since your son has no earned income, there is no earned income credit. That is true for you as well as you note you do not work.
I hope this works out for you...
