Your attitude is part of your problem. You apparently can't conceive that anything you've done has caused the problem, so you're pushing all the blame off to Peterson. Do you want a shoulder to cry on, or do you want someone to tell you the hard truth about what you're doing that's contributing to your problems?
You apparently don't know how an FL die works, if you did you would know that the die itself sizes the neck to a much smaller OD than is necessary and then expands the neck back up using something known variously as an expander ball, sizing ball, expander button, sizing button (Redding's Term*), what Peterson is referring to as the "mandrel", and what you called the "carbide insert". We can quibble about the semantics of calling it a mandrel versus a button, but at the end of the day it's the same thing.
I'm using a Redding FL resizer non-bushing with a Carbide insert
The excessive movement in and out is hardening the neck of your cases. To Peterson's point if you used a bushing die the total amount of movement inwards in the die and outwards over the button would be significantly less, thus work hardening the brass less.
The second factor here is that depending on what the radial clearance of your chamber is you could have the cases moving excessively outwards when fired, which adds even more to the total movement amount. The total movement is what will contribute to work hardening of the case neck and shoulder.
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https://www.redding-reloading.com/online-catalog/28-carbide-size-button-kits
A few cases, after the second firing, split.... After the third firing of the same lot, I had a few more split. When I went to resize them again, I had approximately 5 cases of 55 split the necks. .... Furthermore, I checked my shoulder bump and it was around 2 thousandths with my Hornady gauge.
You did not "bump" your cases in a Redding FL sizing die on the first resizing. If (as the video you claimed you watched told you) your cases chambered without resistance , then when sized in a correctly set up FL die your shoulders should have not moved, or potentially may have moved forward during the first resizing. If you resized a case down that was not fully expanded to the chamber then you oversized the case and there was too much movement on the subsequent firing.
A Forster "bump die" doesn't actually size the body of the case down, and instead sizes the neck and can slightly set the shoulder back at the same time. A Redding FL die will size down the body of the case, which is what leads to the shoulders moving forward on the first sizing if they're still short of the shoulders in the chamber.
It's not hard at all to move the shoulders of a case back 0.002", but it does seem to be hard to wait enough firings until cases actually need it. If you don't wait, you never find the real end of the chamber, and you overwork your brass.
A person may be able to simply neck size after the first firing, as long as the bolt will close without resistance.
The Erik Cortina "Don't Neck Size Your Brass!!!" Fan Club that calls everyone who neck sizes stupid seems to forget the tiny tidbit of letting cases form to the chamber before bumping it an important step.
