If your 21 year old daughter is not a student and earned more than $4,700 you cannot claim her as a dependent on your return.
If you cannot claim her as a dependent, then no, you would not enter her 1095-A on your return.
Did she say someone else could claim her but would not be or did she say someone could and would be claiming her?
If she earned less than $4,700, and you provided more than half of her support for the year, then you would be able to claim her as a dependent for the Other Dependent Credit. If you can claim her then you would need to include her 1095-A on your return. She should not have claimed it on her return as a dependent.
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