My employer says their insurance company won't allow me to drive company vehicle. How can I fix this ?

Ask them why. It is likely the prior driving record. So you probably cannot fix it.

It shows that 30 years after your DUI, you are still drinking and driving.

You are a high risk driver that could potentially cause the company it''s assets in the event of an accident.

You cannot change the facts.

Unless you have access to a time machine, you can’t. 

You can't. You should have thought about that before you decided to drink & drive. That record is part of your record and it will prevent you from driving for a living, or any part of driving while employed. Isn't foresight everything! So's killing people. You got lucky there.

You CAN'T. The insurance company can legally refuse to cover you for ANY reason and YOU can't do anything about it. More than likely, if your record is SPOTLESS for 5 years, they won't care anymore.

Before you comment that my answer is BS, your ATTITUDE is BS. If I were the insurance company, I would refuse to cover the company vehicles at all as long as you were an employee.

The open container violation 30 years after a DUI shows that you learned nothing. There's nothing you can do to force the employer's insurance company to change their position. You present them with a great liability risk, one they don't want to accept.

Couldn't drink that drink inside a building somewhere, could you? Just had to have it in the car. Actions have consequences.

You can’t.  Best you can hope for is for your employer to assign you to a position that does not require driving.   

You can't, too high risk for insurance company to let drunks drive.

Drive your own vehicle.