Yeah, I'm in the same boat with the furry thing. My parents think it's the weirdest thing ever. I'm not sure if I care if my parents find out. I do keep it a secret though. The only way I'd probably be able to go to a con is do wait until I moved out. To keep it a secret and what not.
I'm not sure you can really convence your mom to change her mind. It may be your age, and, well, the yiffing thing. I guess you could show her videos of cons or something like that. You could wait, and go when you're older as well. Of course that will take awhile. Just a thought I suppose. I can't really comment on your sexuallity. That's a whole other ball park.
The best thing you could do is just do what you feel is right.