The trickle charger is not supposed to charge flat batteries, it is supposed to keep your batteries topped up after it has been charged by running or after using an auxiliary charging unit. Which stops the batteries going flat over time. You should also have a kill switch to turn all power off when the MH is not in use. The trickle charger will still keep the batteries charged if wired directly to the Motor Batteries, (the generator would charge the house batteries!)
Hence shore power would not affect the trickle charger and vise versa. The trickle charger can also be left wired in so it automatically switches on and off when the motor is running.
PS, some trickle chargers plug in to the old cigarette light socket, but if you have to turn the ignition on to use the socket, your charger won't work once the ignition is off and the kill switch is off..