I got into an accident a month ago, and it wasn’t my fault. The other insurance will only give me $500 for the KBB value of my car. The cost to repair my car will be around $4000. I do not want to buy a new car and just want to fix my car.
Can I get the other insurance to repair it instead of giving me the cash? Should I hire a lawyer if they refuse?

Yep, they claim your car is totalled, which means it’ll cost more to fix than it’s worth. Sometimes you can buy your car back, but with that much of a difference you’re better off getting another car.