Hi!
I'm a parent (dad), 3 kids, 1 still in high school, 2 out...
First, congrats on telling your dad, and kudos to him for not freaking out and being supportive.
Your mom sounds like she might be more...difficult...having said that, my ex (the kids' mom) and I had an agreement: She knew she was prone to freaking out (and I was known to be calm and reassuring), so when she accidentally discovered our 17yo daughter was pregnant, I was asked to approach our daughter and find out the story...I opened the conversation with "Your mom saw something on the computer..." Once I got her side of the story, I told her it'd be ok and that I would let mom know the details if she (my daughter) wanted (she did).
Her mom was very accepting, but was upset that her daughter wasn't comfortable telling her this big secret in her life. The point of this is, maybe ask your dad for help or suggestions on how to break it to your mom?
Remember, sometimes our fears are more scary than real. Hope it all works out.