Adulting sucks.
You rented their equipment without insurance and damaged it. You can’t really be confused why they’re coming after you?
I suspect they contacted the Company/Agent you put on the agreement and were told you don’t hold your own policy, only your father.
Dad doesn’t have any responsibility here.
Any guesses who does?
My shot-in-the-dark?
The renter.
Companies have state minimum coverage of their own regardless of whether you purchase the waiver. But that company will have a subrogation right to recover against the driver.
If the driver has insurance, without an exclusion, then the insurance indemnified renter to the limits of his/her policy - and renter becomes responsible for excess.
We don't have all the info I'm sure.
But most rental companies just state if you don't have personal insurance, or if it doesn't cover, you are personally liable, including loss of use damages and diminished value. An enterprise or hertz may not even ask for policy numbers, just for you to state your deductible. Uhaul asks even less, because the agreements usually contain language letting them recover against you.
Most credit cards have rental protection, but, not for anything with a cargo compartment such as a truck bed, flat bed, cargo box, or van body... they word it pretty tight.
Many insurance companies exclude cargo carrying vehicles you rent because of the replacement cost. When listed as an additional driver via household status on another policy, there's usually restrictions on who can own a vehicle, types of damage/losses, what constitutes a covered even, etc.
So my guess is it goes like this: uhaul says only the trailer had a damage waiver. At least deductible if not exclusions (such as additional driver is only covered when operating a covered household auto) apply via the household driver policy. Renter may be violating some cooperation clause requirement if nonresponsive too long triggering other provisions. Then renter gets left holding the bag for some, if not all, damage.