OK, then it's a matter of priority - which insurance (yours or your father's) will pay the claim.
Liability car insurance coverage
follows a driver no matter what car they are driving (as long as the vehicle was legal (ie. legally registered and licensed).
It depends on your father's auto insurance if they will cover the accident or not - there are certainly insurance carriers and policies who will not cover any driver who is not specifically named in the policy.
Since you are not a "household member" you are not automatically covered under your father's insurance policy.
So your insurance would cover the accident and damages - maybe your father's.
What you should do is file a claim on your auto policy regardless to avoid having your father's insurance rates increase from the accident.
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