Allow me to try to clarify a few things.
Most RV power in campgrounds come as 20Amp, 120V, 30 Amp, 120V and 50 Amp, 240V. I have no idea where this 40 amp comes from.
All TT, FW and MH come in one of the three power configurations mentioned above.
Providing 50A power to a 30A camper will NOT provide any more power. The camper is only capable of using 30A, and has a main breaker to prevent any more power being used in the camper. Over time, this main 30A breaker may get weak, as mentioned, and need replaced. If this is the breaker that is tripping, replacement is a very good idea!
The CONVERTER takes a small amount of this 120V power and converts it to 12V to charge the house batteries and help run 12V systems.
An INVERTER takes battery 12V power ind inverts it to 120VAC. It is only used when shore or generator power is not available. It is rarely capable of running an A/C or microwave for more than a minute before exhausting the battery.