Have not yet struck wrong rudder input in the 737 simulator following engine failure. However several nasty frights training in both military and civilian twins.
When simulating engine failure in the HS 748 I pulled back the throttle sharply shortly after gear selected up (in retrospect silly thing to do but I was young and overconfident). The pilot under training was experienced and the take off was under the hood. Unfortunately he applied wrong rudder before I could prevent it. Aircraft rolled sharply and fortunately I was able to re-introduce power as well as get aircraft under semblance of control.
Same problem when closing throttle on Dakota (military DC3). Instrument take off and pulled the throttle too early for safety. Got away with it due good fortune.
Single engine (zero thrust set on "dead" engine thank goodness) low level go around (again on instruments) during instrument rating instruction using a Duchess. Student pushed up the live engine throttle very fast and at same time he anticipated the expected yaw/roll - except he pushed on wrong rudder. Alarming yaw and roll and although I was on alert for wrong rudder input the student caught me this time. Again got away with it. My fault for allowing the student to get too low to the ground before initiating the single engine go-around. Zero thrust on "dead" engine meant power was available for recovery to wings level. Practice feathered landings and go-arounds are too risky if mis-handling occurs by student or the instructor.
Worst case also in Dakota. Instrument take off from brakes release. In retrospect unlikely scenario but that's how it was in the old days. The student (My Commanding Officer) lifted off and seconds after gear lever selected up he called "engine failure starboard side."
He had lots of rudder and aileron applied and was obviously struggling because aircraft was banking sharp right. He attempted to reach up and hit the starboard feathering button. Luckliy I was able to prevent his fingers from touching the button because both engines were delivering take off power so obviously no engine failure. On taking over control it was clear we needed almost full aileron and lots of rudder to prevent yaw /roll to the right.
I looked outside at the starboard wing and saw that the rubber de-icer boot that runs the full length of the wing, had split asunder and was flapping over the leading edge and playing havoc with wing lift. Hence the roll/yaw moment. Circuit carried out with three quarters wheel needed to counteract loss of lift on contaminated wing. Flapless approach and landing carried out with wing steadily dropping during hold off. I was concerned about effect of flaps with contaminated wing which is why I decided to go for a flapless. Touched down with last of full aileron control applied. Later inspection revealed rubber de-icing boot had perished probably due tropical conditions over several months.