I would like to be able to punish the horses more for their misbehavior, but if I suddenly started to bring whips over to the horse when I'm tacking up and whacking them people will think I am being horrible, especially as no one else does things like that.
A) Using pain as punishment is not cruelty so long as it is delivered immediately after the disobedience and it is released immediately after the point is made.
B) If others in your barn do not understand A above, then they are ignorant and poor horsemen.
Everything we do around horses centers around the infliction of discomfort (to some degree) as persuasion for them to do what we want and the release of that discomfort as a reward for their obedience.
The use of aids (bit, leg pressure, spurs, whips) all inflict discomfort to make the horse go, stop, turn, etc. When they do what we want, we release the pressure from our aids.
Honestly, after reading this whole thread, you seem to be under incompetent instruction and mounted on sour, ill mannered horses.
If I were you I would go somewhere else. If I were your father, I would take you somewhere else.