Feeling betrayed is the pits. My stepmother is a gossiping type. Life is better, when there is space. I'd also feel leary of an invasion of privacy like you've experienced.
Just live your truth. Who needs the kick 'em when they're down types? Do their opinions, truly matter, when this is the type of character they display? In the long term, most certainly, not. In the short term, may sting a bit.
Are you coming clean to your dad, about SH?