"They lived with me 6 months of the year "
They needed to have lived with you MORE than half the year (183+ nights in your home)
If you meet that requirement, you may claim your grandchild. It does not matter where her support came from.
Your daughter must qualify under the qualifying relative rules (see below), unless she is under age 19 or a full time student under age 24. Then she qualifies, under the qualifying child rules, the same as the grandchild.
