Yes but your question indicates that you don't understand insurance If you occasionally drive an insured car with the owners permission and have a valid drivers license you will (with very rare exceptions) be covered by whatever coverage that has been placed on the car.
I doubt you have any coverage whatsoever from your Mom's policy when driving a car not insured on her policy. If you were driving your father's car with his specific permission you may be covered under his policy. To be sure he would have to check with his agent.
Let's understand that you have no insurance whatsoever.... Your mother has insurance on her cars and you dad has insurance on his car(s). Your mother is covered when you drive her car and you are partially covered when you drive her car. The fact that you are listed as a permitted driver does not make you an insured driver within the legal definitions within the policy.
Probably. Your father's insurance probably covers anybody who drives the vehicle with his permission. You need to make sure you're not listed as an "excluded driver" under the terms of his policy.
He may have signed something that says you specifically have no coverage driving his car, or anybody under 25, or anybody other than him, or something like that. You probably would have coverage problems if the car was "made available for your regular use" (meaning you had access to the keys and implied permission to use it anytime you want) if you are not listed on his policy. If it is occasional permissive use and you're not specifically excluded in some way you're probably okay.
Generally your dad's car insurance will cover any licensed driver who has his permission to drive it. Check with his insurance agent, though -- there may be a "specific exclusion" for you or other persons who have poor driving records, etc. I suggest asking for an email from the agency stating that you are insured under his policy to drive his auto. You also may have coverage through your mom's policy.
Have 3 kids and 5 grandkids and several autos.
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