What if you are driving your mother's car she has full coverage and you are not on the policy and no license and you wreck the car?

not on the policy=not covered. no license=not covered.

While this is basically true, you need to know some of the reasoning, so the issue does not recur.

Insurance is a transaction where, in return for money (the premium), the insurance company agrees to assume certain losses caused by events(risks) defined in the policy (a written contract). The alternative to having insurance for a risk is to be personally financially liable for damages resulting from the risk.

For the insurer to accurately determine what to charge for assuming a risk, it needs to know the risk factors. In the case of car insurance, these include the make and model of the car, how it is used, by whom it is used (authorized users), the experience/age of the drivers, and various other factors. While insurance rates (from which premiums are derived) are regulated, state insurance regulators recognize the foregoing as valid factors in setting rates.

In your case, your mother's premium was apparently set based upon her being the only driver. You were not a licensed driver, and therefore, right off of the bat, cannot be legally driving (unless you were learning, with an adult in the car). Assuming that not to have been the case, the insurer could not factor into the risk it was assuming a premium for you, and therefore, it denied coverage. There was likely also a provision in the policy stating expressly that there would be no coverage for a collision when an unlicensed person was driving.