Im sorry youre dealing with this ❤️❤️
Honestly my policy with people like this is tell them nothing and let them find out naturally, maybe a sprinkling of not hanging out with them as much
But this doesnt seem viable for your situation, so idrk. I hope it goes well, do get as much backup as you can. Hopefully your dad might change his tune when its his kid, or maybe he'll learn over time. Noone can know, but i hope for the best!
I will say that people being anti trans in my life stopped me from transitioning for years, and is a strong reason why i still get anxious in public and stuff like that. My advice is dont do that lol