Dear Rajathi, your daughter will have the domicile of Karnataka. Now most States scrapped the Institutional quota for Candidates who pursue their 10th and 12th from their State to favour Candidates of their State. West Bengal leads on that front. Now to hold domicile of Tamilnadu, a Candidate needs to hold the following eligibility criteria.

1. He/She should be a native of Tamilnadu
2. Students belonging to another State cannot claim nativity of Tamilnadu
3. A native of Tamilnadu who has studied from Class 6 to 12 outside the State needn't produce the nativity certificate. He/She is eligible for Tamilnadu domicile.

Regarding Karnataka Doimcile,

1. The Candidate should have studied in Karnataka for a minimum period of 7 years in a Govt. Recognised Institute
2. Candidate should have passed 11th and 12th from a Govt. Institute located in Karnataka and either of the parents should have studied in Karnataka for a minimum period of 7 years.
3. Candidate who has passed the qualifying examination from an institute located outside Karnataka can be eligible for Karnataka MBBS 2018 admission if either of his/her parents is a domicile of Karnataka state. In this case, the mother tongue of the candidate or either of the parents mother tongue should be Kannada, Tulu or Kodava and the candidate has to give a Kannada language test.

So in this case, your daughter's domicile will be clearly Karnataka and not Tamilnadu.