I gave my family six months to get used to the fact that I'm transitioning, and then I told them that I don't want to hear the wrong name or pronouns ever again. I said that if they use the wrong ones I will correct them every single time - in public if necessary - and
they will be the one looking like a complete idiot who can't tell the difference between a guy and a girl.

I also told them that the fact I'm trans is private and they're privileged to have this info, but they have absolutely no right to discuss it with anyone else.
If they refuse to use the right terms or if they invade your privacy, make
them feel uncomfortable about getting it wrong. You'll feel less dysphoria when they do it and they will change their behaviour.