Hi asm_2003,
http://www.legis.state.il.us/ilcs/ch625/ch625act5articles/ch625act5Sub39.htm explains the mandatory insurance provisions in Illinois:
Sec. 7-601. Required liability insurance policy.
(a) No person shall operate, register or maintain registration of, and no owner shall permit another person to operate, register or maintain registration of, a motor vehicle designed to be used on a public highway unless the motor vehicle is covered by a liability insurance policy.
You are also required by law to carry evidence of insurance in your car.
I'm afraid neither you nor your father have a defense. In my state offenders are often given the option of community service in lieu of fines and sometimes fines are lowered or tickets dismissed if you can show you have current insurance coverage. I'm not sure on IL laws regarding these options.
I hope you don't mind if I express my opinion. If you look at the reality of your situations, 1) going 14 mph over the speed limit in a school zone, and 2) using 'unawareness' as an excuse, it's clear that you are, at the very least, an inexperienced driver or at the worst, you have no respect for the law. I prefer to think you are just young and have a lot to learn. Driving is a privilege that comes with huge responsibilities.
Law enforcement officers are on the lookout for those people who are breaking the law. In order to ensure that you are no longer a target I suggest you drive responsibly obeying all the laws, then you won't have anything to worry about and you'll have more money in your pocket.
Although it's water under the bridge, this section
http://www.legis.state.il.us/ilcs/ch625/ch625act5articles/ch625act5Sub51.htm covers school zones. The 7 a.m. time is in effect because parents are dropping them off on the way to work and to accommodate public transportation schedules. It's quite reasonable to believe that kids would be arriving at school between 7 and 7:45...they don't all arrive 10 minutes before class starts.