A little bit of AC distribution info. A 50 AMP panel will have two hot lines feeding every other breaker. The coach builder will configure the panel to balance the total coach electrical load between the two hots. AC's will be split, microwave and water heater will be on different feeds and the outlets evenly spread around. Loose one of the feeds and you loose half the coach.
Since you have full power when plugged in problem is either the generator, the transfer switch or even the wire between the two. Probably safe to say the mechanical side of the generator is functional considering you have partial power just need to pin down were the problem is.
I have a 50 amp configured coach but a 30 amp generator. My breaker panel is configured with the rear (first owner install) AC and the water heater on the hot that is only active when on shore power. My generator only has one output into the transfer switch which powers only the front AC and outlets. A bit of a reverse of what is occurring here.
Good luck.
Also the your furnaces run off of 12 VDC which is why they still work.