Suburban Water Heater

Hopefully the hot water heater had water in it when the AC heating element powered up.

The hot water heater has a 1,440 watt heating element and pulls 12 amps by itself. Much else on at the same time will trip a 15 amp breaker.

There are, far as I know 3 main types of breakers (Plus a couple sub types that won't affect this thread)

Standard. Trip if overloaded current wise
ARC-FAULT. Trip if they detect an arc on the down line in addition to current
GFCI Trip if there is ground fault (in addtion to current)

And how big is the shop breaker?

It may be that there is too much draw. if shop breaker is 15 amp Heater pulls about 12.5 (it SHOULD hold but it's borderline) but the Fridge draws around 3 and the converter up to about 10.. CLICK CITY even a 20 amp will go if that happens.

Arc fault a bad heater thermostat (relay on an Atwood) may do it.
GFCI.. Well I've heard of issues with the heat element the insulating jacket can crack. causing a ground fault.

IF it turns out to be the heat element (Rare but can happen) May I suggest you go to a 1500 watt 240 volt element..(that's 375 watts at 120 volt) takes a bit longer (4x) to heat the water but also less likely to trip a 30 amp park breaker.

What size is the breaker in the RV? And what size is the one in the shop and is there anything else plugged in and running on it?

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Sounds like he is pulling too much power from the circuit in the shop. I am assuming he has a 30 amp trailer connection I am also assuming the shop circuit is 15 amps (1800 watts) or 20 amps (2400 watts). The refrigerator draws about 600 watts, the power converter that charges batteries and runs the 12v appliances can pull another 600 watts totaling 1200 watts. Adding anything else of 120 volts doesn't leave much for the water heater. So the shop breaker will keep tripping.

Another thing that could be making the shop breaker trip is if there is a regular extension cord which is only rated for less than 15 amps plugged in between the shop receptacle and the trailers 30 amp plug and cord. The longer the length of wire the less amperage can pass through so the appliances will try to draw more amperage resulting in the breaker overloading and tripping. If the bresker doesn't trip the wiring will over heat and cause a fire.