Dodge Hitch Covers

I hit my dad's expedition with my Dodge Ram and caused about 1500 dollars in damage to my Ram, as estimated for parts and labor by a collision center, I hit the expedition's hitch which caused damage to me but barely a few scratches on the expedition. The expedition doesn't run, and is not even registered or insured. My dad is aware of the situation and has no interest in fixing his car and will not report me to the insurance or police. We have and still are on good terms.
I have liability insurance, so it will not cover damage to my vehicle.
My insurance policy expires in two weeks.
What if I update my insurance with collision and comprehensive coverage that will cover my vehicle. Then I report that I hit an object and have them pay for it.

Would this be cheaper in the short and/or long run than paying to fix out of pocket?
Is such action above illegal, unethical, and/or against policy?
I live in California and have Progressive insurance.