CDL School starts on Monday!

What??? Either you're kidding or something is being grossly misstated.

(as listed in your examples)
You're saying , if the trailer is too tight on the left... turn left.
Then you say, if the trailer has too much room on the left... turn left.

You can't use the "turn towards the problem" rule... if you swap the type of problem (ie, too close,, too far) on the same side of the trailer.
Because those are opposites... and require opposite steering action.

A good consistent foolproof rule is... turn the steering wheel in the opposite direction you want the trailer tail end to go.
Or (easier for newbies)... grab the bottom of the steering wheel and turn it towards the direction you want the trailer to go.

 

I understand. Actually, I began with a 'modified' style of holding the wheel while backing.
I hold it by the 3 o'clock position, and if I want the trailer's rear to go left,, I turn the wheel downward (clockwise).
If I want the trailer to go right,, I turn the wheel upwards (counter-clockwise).

Same "turning direction" as what I stated before,, but just holding the wheel in a more natural position, for me.
Also helps me avoid 'over-correcting'.

 

It's hard to advise on your particular situation/problem, without being there to see what you may be doing wrong.
So anyone here can just give general recommendations.

If I assume you're talking about only straight line backing, then a lot has to do with speed as well as the amount you turn the wheel.
You should maintain a VERY slow continuous speed for your initial practices, and smooth slight 'corrections' with the wheel as you back.
Don't wait too late to apply the corrections, and don't over-correct either.

In docking, it may also help, especially in cases where there are lines, to watch the path of your trailer tandems, and not just the rear of the trailer.
The position of your trailer tandems (way forward vs way back) makes a big difference on how the trailer reacts to steering input.

A lot also matters on how much "off" you get and how much room you have before you get to your target stopping point.
Sometimes a pull-up is required to "straighten out", if you don't have the space behind you to make the needed correction.

As for parallel parking... I used to use it more than you imagine. Getting off to the side where you have parked vehicles with only a 'slot' open.
Or in certain rest areas or truck stops, where the main lot may be full, and you have to park on the sidelines.

 

** I was going to edit/add this↓↓↓ to my post above, but decided a separate post would be better, so you didn't miss it.

I had missed a critical thing you said. You have been stopping when making your steering corrections? Am I correct?
THAT will put you always 'behind the 8-ball', and make things much harder, imo.

Your trailer takes time and distance to react to directional changes. It can't do that when stopped, and it then takes time/distance to 'start to do it' once rolling.
The 'reaction' of the trailer is highly dependent on speed. That is why I suggested before to proceed at a VERY slow consistent speed while backing.
It must be a slow enough continuous speed to allow your abilities to 'keep pace' with steering corrections.

As you get better, you can increase your backing speed, and be able to put that trailer anywhere you want.

 

Best thing to do when straight backing is to get your foot off completely the clutch pedal once you've engaged the clutch and let the truck roll back without stopping. Don't ride the clutch. Let the truck roll. If the trailer drifts left, turn no more than 1/4 turn left. If it drifts right, turn no more than 1/4 turn right.

Both Town Drunk and KW Cajun are correct. If the trailer drifts in either direction, that's your problem so you turn towards your problem. If the trailer is too tight on the left, but it's going straight AND you want to center the trailer on the lane, turn 1/4 turn to the left, and vice-versa. Remember, if the trailer is going straight, you really don't have a problem. If it ain't broke, don't fix it. Better to be tight on either side and be going straight than to try and fix this and end up encroaching with the tractor wheels. If you really want to fix that, stop and do a pull up. Me? I wouldn't screw with it.

You'll get plenty of advise here. But, consider that while in school, you want to do what the instructor tells you. Pool from all learning sources, including this board, but do what your instructor wants you to do. In the final analysis, your instructor is your "dispatcher" and "SDM" while in school. Keep that in mind now and you'll have little problems once you get out of school and start working.

I started flying jets for a living 30 years ago and I taught many people how to fly airplanes for 3 years before that (I stopped flying professionally 20 years ago for personal reasons). One thing I always told my students was this; keep your scan going. This way, your deviations will be small AND your corrections will also be small. Same concept applies here. Watch your mirrors constantly and don't fixate on either, especially when backing. Catch a drift as it starts and your wheel movements to correct will be minimal. Even when you're alley docking, you should not have to turn the wheel more than one (1) turn to get the trailer going in the direction you want. After that, is all a question of anticipation and follow through.

Keep posting. It's interesting to re-live school through your experiences!!