Hello ma'am. Yes, your daughter will be eligible to apply for Tamil Nadu seats as well.

For this, " students with a Domicile of Tamil Nadu but have partially or fully completed schooling from 6 to 12 from outside the state, would be required to submit copies of the parents’ documents as mentioned (Birth Certificate, Ration Card, SSLC/ 10/ 12 Certificate. Students will also be required to subm it an undertaking stating that they have not applied as natives of any other state, apart from Tamil Nadu ." Hope your query is answered.