First piece of advice for those considering a coaching career: reconsider. Coaching is a blast and is emotionally incredibly rewarding, but it's physically and emotionally exhausting and doesn't pay much for what you put in. In other words, it's a wonderful, wonderful job when you're in school and your parents are covering most of your expenses, but it's not nearly so wonderful a decade down the line when your injuries take longer to heal and you have to pay bills/rent/mortgage/etc.
Second piece of advice, should you choose to ignore the first: coaches are imperfect. don't strive to be as good as the coaches who coached you; strive to be better. Your coaches' ability is not the end goal; it's the starting line. Sports science has progressed, sports psych has progressed, gymnastics technique has progressed, and society has changed since your coaches were in the sport. I myself am not by any means old; it's been a mere ten years since last I competed, and yet the sports has changed enormously since I was an athlete. If I were to teach my students the way my coaches taught me, it would be inadequate at best and negligent at worst.
If you came up in the sport as one of my students, then your absolute first assumption should be that you can do it better than I did. Do not even question this assumption. Your job is not to coach your students as well as I coached you; your job is to do it better. The way I coach is most-assuredly wrong, but it's less wrong than the way my coaches taught me, which is less wrong than the way their coaches taught them. Your job is to be less wrong than me
Third: look two years ahead. In other words, if you are coaching a group of level 4s, don't look to build great level 4s; study your gym's level 6s. Look for what they do well, and try to emulate and replicate that; even more importantly, look for the things they struggle on, and try to find ways to preemptively avoid those struggles.
Fourth: technique should be driven first by mechanics, and second by aesthetics. In other words, your first priority in training a new skill should be to optimize for mechanical efficiency; perfecting form comes after (though not long after). While an understanding of proper form and tightness and body control should be introduced as early as possible, it is extremely common for form errors to have an underlying mechanical cause.
For example, suppose you have a kid who is piking down at the end of a back layout. Rather than trying to get them to remain extended in their layout, it may be more effective to try to build more power on the takeoff, allowing them to complete the rotation earlier without having to pike down at the end. Or suppose you have a kid who bends their knees in a cast to handstand; rather than just trying to get the legs straight, try to build their confidence and control and strength to the point where they can make it to handstand without feeling like they have to bend their legs to get there.
For every error, there is a reason for the error, and that reason most likely has to do with either mechanics or psychology. If your competitive-level athlete (assuming he or she learned decent basics and understand the concept of a tight body) is making a form error, they are not doing it intentionally; they are doing it because, in the middle of the skill, it intuitively feels like the best option. Rather than looking to fix the form error, you will generally find more success by looking to correct the source of that intuition.
Fifth: for every skill, train the crash first. Whether you're working on a handstand on floor or a giant on bars, athletes will be more confident and consistent and clean if they understand how to bail out of the skill if something goes wrong.
For example, suppose you want a kid to hold a handstand on floor. The kid will never achieve vertical until they are equally confident falling either forward or backward; this being the case, they should learn how to step down, and how to either forward roll or quarter-turn-bail.
Sixth: pick up a copy of Championship Gymnastics by Gerald George.
