Congrats, man. You're lucky you have a mom who actually isn't emotionally unstable; when I came out to my mom, she started crying. Every time since when I've brought it up, she's either started crying or yelling. It's fun.
As far as your dad, I thought mine would be the worst one as far as accepting me... while he doesn't accept that I'm trans, he doesn't harass me in the slightest about it, unlike my mom and brother. He's actually become a pretty decent guy, whereas prior to my coming out, he didn't talk to me at all except to criticize me for one thing or another. He has 3 other sons, so I kinda wonder if he's changed his attitude toward me because, whether he likes it or not, he sees me more as a son now, and it's easier for him to relate.
Your dad might surprise you. At least you've got one person who's fairly understanding.
SD