ELECTRIAL HELP FOR AC
It sounds like the most likely problme is a combination of the air conditioner drawing too much current and bad breakers on the RV distribution panel. But, the problem may also be that there is some other load that is drawing enough that with the air conditioner as well, the two together cause the power to overload the genset or the breaker in the house. You don't say what the size of breaker is that is being tripped, as compared to those on the power distribution panel of the RV? I suggest that you try opening all of the breakers on your RV's power panel except the one for the air conditioner. Then test the air on both shore power and the genset. If all other breakers are open, you will then know that the air conditioner is the load causing the problem. To go much farther once you know that, you will need to have a clamp on, amp meter to know just what the load is at different points in the circuit.
A few questions that might help. What is the rating of the circuit breakers for the air conditioner? Do you have one, or two air conditioners? What size of genset do you have and what make is it? Do you have 30A or 50A shore power cord and is it plugged into an outlet that is rated for the full supply that it can draw?