It is halachically permissible to uncover one’s hair in the privacy of one’s home in front of immediate family members, including one’s father.

As with many questions of tzniut, communal norms differ. In practice, you should be sensitive to what is deemed acceptable in your and your father’s communities.

We recommend reading more about hair covering in Understanding Tzniut and Responsa on Contemporary Jewish Women’s Issues by our site’s founding posek, Rav Yehuda Henkin z”l, and at the Deracheha website here and here.