Lots of good information here but first things first.
Forget about what is turned on or off in the coach.
What else is connected to the circuit in your garage?
Are you certain that it is a 20 amp breaker? It might be a 15 amp.
If nothing else is connected to the outlet circuit in your garage, disconnect the extension cord and start the generator in your coach.
Do the ac outlets work in the coach? If your outlets and other appliances work properly using the generator then more testing will need to be done to see if you have an overload on the garage/motorhome circuit or a dead short somewhere between the outlet and the transfer switch in the coach.
Turn the generator OFF then make certain that your transfer switch is in the OFF position. Plug the extension into the outlet in the garage. If the breaker pops, you have a dead short between the transfer switch and the garage outlet. Start looking at the a.c. connections in your coach.
For most 120/240V systems using cords or cables of adequate ampacity, voltage drop is not a concern unless cable lengths are well over a hundred feet or the outlet voltage in your garage is less than 110 VAC.
2004 Damon Escaper 4076