watts = volts * amps OR w=v * a
Your generator is probably 7,500 watts and creates a 120 volt electrical current. Thus, your generator is putting out
7,500w / 120v = 62.5 amps. These numbers apply to the generator: 120 volts; 62.5 amps; 7,500 watts. In addition, your generator puts out power on two legs (two wires) with each leg (each wire) getting half the total amps produced - 62.5 amps / 2 = 31.25 amps on each leg or wire.
The shore power cord is 15 amps at 120 volts. Therefore, your shore power is 15a * 120v = 1,800 watts.
These numbers apply to the shore power: 120 volts; 15 amps; 1,800 watts. The shore power comes all on one leg - 15 amps on one wire.
Looking at your generator - It creates 62.5 amps. Air conditioners usually require from 13 amps to 20 amps; 13 to 15 amps after start up and upwards of 20 amps at startup. Just like driving a car you have to step on the gas to accelerate, then you can let off the gas to maintain speed or coast. Thus, your generator can run more than two air conditioners. The engineering design is such that you have two air conditioners (2 * 15 amps = 30 amps) and still have power to operate other devices in the coach (like the TVs, microwave, water heater, etc.) - 62.5 amps - 30 amps = 32.5 amps extra for other devices. As noted above, there are two legs each giving 31.25 amps. Your two air conditioners run from both legs - one runs from one leg and the other runs from the other leg.
Looking at the shore power - It is only 15 amps all on one leg. Since one air conditioner requires upwards of 20 amps to start up, there is a high probability that starting only one air conditioner will kick out the shore power's breaker. In addition, there are devices in your coach which use a little power at all times. For example, the engine's brain (ECM), the inverter/charger, other sensors, etc.
I don't know why the shore power needed to be disconnected prior to starting the generator. To my knowledge, when the generator gets going and provides power, then the transfer switch will transfer away from the shore power and to the generator power as the power source for the RV. You didn't indicate which breaker kicked out when you started the generator.