If you have “full coverage” –this usually means you have purchased collision coverage—Good for you. This means if you cause an accident with another vehicle, or just lose control and have a single car accident, your collision coverage will pay to repair your car after you pay your deductible- usually $500 or $1,000.
If the accident is clearly not your fault—you get hit in the rear for example, you may not even need to use your collision coverage, because the insurance for the at-fault vehicle may immediately compensate you.
If liability is being disputed, in a he-said-she-said scenario, neither insurance company is eager to pay for your property damage, I always recommend using the collision coverage so you can get your car repaired immediately, and let your insurance company deal with the at-fault vehicle to get your deductible reimbursed. If you are not responsible at all, you should get your entire deductible back. If you are deemed to be 50% at fault, you will get 50% of your deductible back.
If no collision coverage, and you are not happy with the percentage of fault allocated to you, you can reject the offer from liability carrier and sue driver and owner in small claims court if PD under 5K.