ASweetOldMan,
This is actually fairly common, and I have often seen this in people, some so bad that they physically become unable to to board commercial airliners.
I think you are managing to beat others with the fact that you understand the irrationality of your inner argument. Unless you have seen shoddy maintenance on the plane that you are flying, then why worry?
Something that may help get your mind at ease, is the fact that the C172 (amongst others on the scene) are very well built, easy to maintain, robust and I cannot recall any catastrophic structural failures relating to wings on any C172, and the few that I have found were directly linked to bad maintenance, with clear visible signs for months (not hours) that things aren't quite right.
During the spin the g load is essentially one so there is no excess
loading. But during the recovery you can generate 2 or more g’s depending on how aggressively you pull out of the dive. In the utility category (which yours is in) my C172 POH states that I can pull +4.4Gs to -1.5Gs. These limits have considerable margins (for certification) which have been thoroughly tested. Even at the upper limit (which I doubt you'll ever pull), and beyond that, there is no certitude of the wing "breaking off" as you say. There may be damage, which may require maintenance.
So you would likely be pulling less than 50% of the certified G force of the aircraft, as well as of course considerably less than the absolute limit.
Try to look at the facts and figures - and realise that there is no more risk in spinning a plane, as there is just getting in one. Especially if you do not think that piloting skills is an issue!
I hope this helps, and good luck with the spins!
Best Wishes,
Alex