FWIW, my insurance went up $5/month after I totaled my first FZ6. I used the insurance money to buy the exact same model (used). All I told them was that a small animal ran under my tire and made me crash.
I can't imagine your rates would double after an accident... you pay for insurance specifically for the situation you are in now, and if the fact that it's your dad who was riding it is an issue, I'd tell them I was riding and a squirrel ran under my tire and made me crash mid-corner.
Why would your rates be jacked up (doubled/tripled or what not) in such a case? it was an accident and you weren't at fault!
David offers some great advice, it comes from experience!
I'm not sure if your dad's insurance will cover it, but I bet yours will.