No, your grandsons don't qualify you for the $500 Credit for Other Dependents because they didn't live with you more than half the year.
Please see the TurboTax Help article What is the $500 Credit for Other Dependents (“Family Tax Credit”)? for more information.
Note: The "exceptions" to time lived with you referred to in the article are temporary absences for special circumstances, such as school, vacation, business, medical care, military service, or detention in a juvenile facility, count as time the person lived with you.
