They changed the rule on dependents a while back, you know.  Which of the four requirements for "qualifying child" do you think they don't meet?  

And it's clear to me that none of the children is providing more than half his or her own support, so I don't think that's an issue.  For head of household (or qualifying widow), the mother may not be paying more than half of the household expenses, because the children combined are kicking in too much.  But you don't have to be HoH to claim EIC.