While it can vary by your insurer, I would recommend getting your daughters' their own policy and simply paying the bill. Because you own the vehicles, you should be added as the additional interest to the policy.
If you're on your own policy without your parents, it's unlikely they would be sued if your coverage is exhausted after a car accident. Because you're considered an adult, regardless where you live, you would be sued if you were found liable - not them.
The zip code where the vehicle is primarily kept is what needs to be used for insurance purposes. Depending on your age, company, and residential state, you may have been able to stay on your parent's policy, but since you now live off-campus you will have to use the address where you live.