The ticket was for speeding, not for lack of insurance. In all scenarios that I can think of, I will have to show proof of liability insurance to resolve this case
Why would you have to show proof of insurance?
Please be specific.
The why is important in determining the how, as well as the answers to your last two questions.
If you need to show proof of insurance for the car you were driving at the time of your ticket, you'll need to pursue your efforts to get the documentation.
If you need only to show that you are insured now so that you can sign up for defensive driving without travelling to the hearing, then it might suffice to show that you are LISTED on your father's policy.
That's why I'm asking why you need to show proof of insurance.
If you don't know, you'll need to find out.
Otherwise, just pay the fine if paying the fine eliminates attending the hearing.