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Hi, Renee. Due to the newer IRS qualifications for "Qualifying Child" and "Qualifying Relative", it has become slightly more difficult to determine dependency.
According to the laws, your grandchildren are not eligible to be "Qualifying Children" for you because they do not live with you. They would be eligible to be "Qualifying Relatives" for you; however, in order to be a Qualifying Relative for someone, you cannot be a Qualifying Child of another person. They would, realistically, be Qualifying Children of their father, even though he does not file taxes.
Also, in order to claim a dependency exemption for someone, you must provide at least 50% of their support.