After switching the brake/throttle, and steering servos plugs

You should be able to control the throttle with the steering wheel.

You should be able to control the steering with your trigger.

I don't know what you mean by "twitching" it should move smoothly.

The problem not being able to properly turn in one direction;

IF it is the servo the issue will still continue to happen ON THE STEERING in the same direction even though you are controlling the steering servo with the trigger.

IF it is the transmitter or receiver, The throttle (now being controlled by the wheel) will only work properly in one direction..