There is no restriction on marrying in a family Gotra anywhere in the Hindu marriage act. In this case, two adults of the same gotra can marry, provided they are not in a Spinda or Prohibited relationship. But your relationship is not under it, you can marry your father's sister's daughter with the consent of your family.
As you said, that girl is the daughter of your father's mother's sister's daughter, so this relationship will not be considered prohibited so you can marry with her.
Marriage cannot occur in forbidden relationships. Brother-sister, uncle-niece, aunt and nephew, brothers' children, real brother and sister's children, maternal uncle and niece, grandfather or maternal grandfather's brother or sister, grandmother or grandmother's brother or sister, brother's wife Prohibited relationship Come under the purview of and in such a relationship if someone gets married then it will not be valid. Spinda relation cannot marry. That is, if a boy or girl wants to get married in the 5th generation of the father and the 3rd generation of the mother, then she cannot get married. This is called the Spinda relation. However there are exceptions to the Prohibited relation and the Spinda relation. If there is a custom of such marriages in a community then it can be married. Like in many areas there is a tradition of marrying a brother's wife. Similarly, the marriage of maternal uncle and niece is prevalent in many places in South India. These marriages are valid despite having a prohibited relationship.