I agree in one area...when I was training on twins, be they piston, turboprop or the Falcon, the 'correct' rudder peddle was never going to travel backwards more than the length of the hair on a Bee's dick.
I never slam any control anywhere...if you wanted to end the excercise in a 'hurry' smoothly moving the mixture back to rich while controling yaw gave you full power very quickly. The fact that the throttle is 'wide open' means only one thing, there is little to no impediment to air being sucked into the cylinders by the pistons. The prop is windmilling, the magnetos are sparking, smoothly restoring the mixture restores power smoothly.
During the course of an endorsement you do get to know what the trainee is capable of and thus the engine failures get a LITTLE bit more testing near the end. But at NO POINT in a CAR 3/FAR 23 piston twin do you start pulling mixtures or closing throttles at 20' with the gear down....unless there is LOTS of runway and you WANT the trainee to land straight ahead. Personally I have never been blessed with training runways that long.
For readers not yet twin endorsed or low time ME.
In my view the only way to conduct a takeoff in a piston twin is;
Assess whether the aeroplane should fly with an engine failure after gear retraction...most will at reasonable weights and reasonable temps. Some have enough performance so you can fly away even having to retract the gear after the failure...Barons, C310s etc...I wouldn't like to try in a Duchess at MTOW....or in ANY piston twin at 40 deg C.
Ensure FULL power is attained early in the takeoff roll.
Fly the aircraft off the ground as soon as it wants to fly.
Accelerate in a VERY gentle climb to at least Vyse+10kts. Note I am NOT advocating flying level at 2'!!!
When you move your hand from the throttles to retract the gear you are committing to fly. On a short runway that might be as soon as you have a positive climb and on a long runway it might be 50-100'. If the engine fails before this control yaw and close the throttles and land. Too many pilots break this rule and end up arriving inverted.
Climb out at Vyse+10-20kts or cruise climb. Speed is ESSENTIAL not altitude. DO NOT reduce power to some BS 25/25 setting...leave everything all the way forward.
At the higher speed you'll need less rudder to control yaw and you have 'ample' time to carry out the memory items and assess whether the aeroplane will actually climb away and allow a circuit and landing while you gently raise the nose and climb with the speed VERY gently reducing to Vyse.
When the airspeed falls to Vyse you lower the nose and peg it...trim and assess. If you are descending start looking for something soft and cheap to hit.
At this point if you are flying level, or just barely climbing, you can start to fine tune things a little to either achieve some climb or maximise what you are getting. Raise the dead engine up with about 5 degrees AOB...don't get paranoid about AOB just raise the dead engine 'a bit'. This effectively reduces the 'arm' through which the assymetric thrust is causing yaw and will allow a little bit less rudder which means a little bit less drag which means a little bit more performance. It may turn 100'/min down into level, level into 100'/min climb or 200'/min climb into 300'.
Climb in a straight line and get at least 4-500' under you before you even think about turning....yes if there is a hill in front miss it
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When you have a minimum 500' or higher, if you're in a good performing aeroplane lightly loaded you might climb to a proper circuit height, lower the nose and accelerate. Reduce power a little if you can and trim the aircraft. At this point in MOST light twins, even the very light twins like Duchess, you should be able to happily cruise at 100+kts with less than full throttle.
Having achieved level flight return to land. At this point turning either way is ok but you may get marginally better performance turning into the live engine...the main thing is a balanced turn.
On base and finals don't be in a rush to slow down to much and definately don't shove the gear out turning base and fly like you might on two engines. Curving around base at Vref + 20kts and slight reduced power at 400-500' should have you comfortably around blue line speed if you need to GA. At 300' on finals select gear down and maintain power and ROD...the gear will start you decelerating nicely towards a NORMAL Vref either flapless or with only approach flap.
At this point you are NOT going to go around!!!!
From here on you are just playing power off against the desired speed reduction to arrive at the round out and flare at a normal Vref (maybe a few knots faster) and then close the throttle in a normal way and land in a normal way. You do NOT land at 'Blue line' speed and Vmca is irrelevant. At typical appoach power settings using the above technique you will stall long before reaching 'VMCA'. Vs is not affected by being on one engine so you're landing speed is not effected either. Above I said you might land a few knots faster than normal. I say this not because a few extra knots is required because it is not...but on one engine you tend to hang on to the speed subconciously and a few extra knots is not worth worrying about or trying to lose by any means available...just land a few knots faster and be happy.
You shouldn't but if you do end up a little lower than you want you have the extra speed in hand to gently raise the nose and correct without having to add any, or at least much, power.