All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
You did not mention the reason why your father does not allow you to wear this type of clothing at home.
In any case, obedience to parents is not an obligation in an absolute sense; it is only an obligation when there is a benefit for them while there is no hardship on the children, as stated by the scholars. For more benefit, please refer to fatwa 131695.
Accordingly, if your father has a valid reason for not allowing it, then you are obliged to obey him. Otherwise, it is permissible for you to contradict him, but as long as you are able to be kind and dutiful to him, do so in order to earn his pleasure and avoid his wrath, and close the door of the devil so that he would not lead you to some kind of conflict with your father.
For more benefit, please refer to fatwa 88123.
Allah knows best.