Did you actually try and use both plugs at the same time, or did you just plug in a 20 amp outlet tester? We need more details.
If you only checked with a tester, you will get an error because of the Honda's floating ground. The grounding circuit is only connected to the generator ground terminal, to the frame of the generator, the metal non-current carrying parts of the generator, and the ground terminals of each receptacle. But, it is not connected to earth, so a tester will read a fault. I use both outlets at the same time with no problems. You just have to be careful not to overload the generator.
If you actually tried running the two trailers, with the converters of both rigs charging batteries, running a bunch of lights, a couple of TVs, etc., it would not be a stretch to say that the generator might have been in an overload condition.
Preface the following with the fact that I am not an electrician or electrical engineer, it is just info that I have gleaned from the internet, reading the manual, etc.
On the Companion unit, the 20 amp circuit is protected by a traditional type of circuit breaker.
The 30 amp plug is not protected by a circuit breaker, that outlet is protected by the electronics in the inverter unit, which analyze the power demands and will disconnect the outlets when the total demand grossly exceeds 2000 watts, leaving the generator engine running but not supplying any electricity.
This 30 amp circuit can safely sustain loads over the rated 13.3 amps(1600 watts @ 120V), up to 16.7 amps(2000 watts @ 120V) for a period of up to a 1/2 hour. At these overload rates, the inverter unit will not trip off the outlet and will keep supplying power to the outlet, and can damage the generator, and shorten its life, if allowed to go on for over the 1/2 hour limit. That is why it is important to keep an eye on the overload LED on the front panel if you know that you will be pushing the generator near its limits. The LEDs are difficult to see when the generator is sitting on the ground and you are standing next to it because they project a very narrow beam of light, a big Honda shortcoming in my opinion. You can hardly see them light up unless you are looking straight down the front of the LED bezel. I am thinking of modding mine to be able to see them better from an angle.
Here is a circuitry diagram from the Honda Companion manual:
You can see the circuit breaker on the 20 amp plug, and nothing on the 30 amp plug.
As far as grounding the unit so a circuit tester will read properly, or if you want (or need) to have a true ground in a boondocking situation, you need to hook up a wire to the ground terminal, attach that wire to a metal rod, and drive the rod into the dirt. Technically, if you were to be using an electric appliance hooked up to the generator without a physical ground wire to earth, you could be shocked or electrocuted in the event of faulty equipment. Even though the appliance has a 3-prong plug with a ground wire, it goes nowhere except to the ungrounded generator (and you
in the event of a short circuit), you could conceivably be the path of least resistance! Highly unlikely, but possible.
OK, this post is getting boringly long, so I will quit.