I dove a few times. The hardest thing is actually putting your face under the water and trusting the equipment with your life. It was a big mental challenge to get over, at least it was for me. I felt kinda stupid because the whole group had to come in early because I was going through my air too fast. I could understand her panic, and you are right, experienced divers know how to deal with us rookies.
When I taught diving, I liked to have a couple assistant instructors with me. That way a problem student wouldn't ruin the dive for every one.
I drilled my students HARD in the pool before they ever set fin in the ocean: pulled masks off, turned off their air, pushed them right to the edge under controlled conditions. That way I could spot the panickers ahead of time and be prepared. Some could be trained to over come their fear (it was usually claustrophobia); a few never could. It was almost always a woman.
When training in the ocean, I stayed close to my students, right next to them. The couple times students panicked, they bolted for the surface (to "escape"). I was trained to grab their BC and slow their ascent. If any one didn't exhale on the way up, I was ready to punch him in the stomach. I never had to do that.