When I do a hard turn on controller the car doesn't turn

It might be worth checking your controller calibration. I can't remember the exact sequence - this is from memory. Go to settings > controller > edit your controller settings > calibration > view controller input. You should be able to see the input from all of your controls. Obviously, you'll be looking to check the left stick doesn't go back to zero at full lock. 

Also, just also checking... Is it because your tyres are locking up under heavy braking? This will stop your car from steering.