Jessica:
If you provide at least half of her and her daughter's total support, then it does not matter if your daughter does not matter if she files a tax return herself or not. Since she is your child, it does not matter whether she lives with you or not. It does matter if your graddaughter lived with you.
The public assistance is not considered income for tax purposes, so it is unlikely your daughter will even have to file a tax return at all. If she does file, she cannot claim herself and have you claim her as well. That, by the way, is exclusively her decision whether she claims herself or her daughter. You need her cooperation for you to claim her and/or your granddaughter.]
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