Most transfer switches are wired for generator priority—in other words, once the generator is running, the shore power is disconnected and the coach is powered by the generator alone. (This is assuming you don't have some sort of a fancy EMS, in which case the sky's the limit for what gets powered by what when.)
I don't know why the house outlet breaker would trip assuming the transfer switch is wired and operating correctly. If it's a GFCI breaker and the neutral line isn't being switched properly, the GFCI would probably pop because the RV generator has ground and neutral bonded together. The transfer switch should be switching the neutral with the hot line(s). If the hot is not being switched, you have even bigger problems and would probably already know that something very bad was happening.
As was mentioned, switching between shore and generator power under load is not a good practice.