Yes, if you have collision coverage on your SUV then your auto insurance should cover damages caused by your wife backing into a pole at the grocery store. You will need to pay the deductible associated with your collision coverage and make a claim under this portion of your physical damage coverages.
If your SUV is totaled out by your insurance company then you should be paid actual cash value (ACV) for it. Actual cash value is the fair market amount that your vehicle would have been worth in the condition it was in before the accident.
The way in which the actual cash value (ACV) is determined differs by insurance company to insurance company but usually uses the Blue Book value, cost of purchasing a car in similar condition from a local auto dealer or private party. The condition of your vehicle, mileage, options and equipment are all taken into account when calculating the ACV.
Whether this at-fault accident will cause your auto insurance premiums to go up will depend upon state insurance laws and also your insurance company's guidelines and rating system. You should discuss if this accident claim will affect your rates with your agent who knows your carrier's specific rating system. You can also try contacting your state's insurance regulatory body with whom insurance companies must file their rates with and who knows your state's insurance laws.