I have not had to deal with this issue, so I can't speak from personal experience.
Your father is forcing you to choose between his idea of who you are and who you really are. If you tolerate this behavior, it will never change; and it is damaging to you personally to tolerate it.
The only way to win this game is to not play. One way or another, whether you tell him personally (better) or let him know by telling another family member, he has to know that you will not tolerate being treated with such an appalling lack of respect. He wouldn't tolerate being treated with this degree of disrespect in his life; and, if there's one thing he will understand about your transition, it will be this: you will not tolerate being treated with disrespect by anyone. And he won't believe it until you cut him off. And whether he agrees with you or not, on some level, he will respect that.
I suspect your brother and other "little dogs" in the family are taking their cues from the "big dog" (your father). Stand up for yourself. You don't have to be rude or unkind about it; just firm. To permit this behavior while continuing to associate with him shows a lack of conviction and/or self-respect, and your father sees it that way.