No way are you overreacting, my heart goes out to you. I am not highly experienced with regard to covering / breeding, but i do have common sense!
When we have covered mares, we always used a `teaser`- a little pony stallion to ensure that the mare was in season and willing (poor pony never actually got to do ought- he stood about 11hh!).Only then if the mare was ready,the stallion would be led up to the mare by an experienced handler, with another experienced handler holding onto the mare wearing all the correct gear, both horses and handlers for safety and the covering took place. Keep your chin up, everybody learns from their mistakes, i`m sure you are not alone