That connector with the integrated shutoff ought to work, and having the ability to connect to the trailer cylinder is a good idea. I don't know about the Champion but my Honda propane conversion leaks a little propane into he carb so I always use the shutoff when its not running.
lostagain's recommendation is a good one too, and I'll add another ever better reason for using a separate cylinder. That's so you can place the genny and cylinder at a distance from you and your neighbor's campsites. Keeps the noise and exhaust smell down as low as possible. And if you're using the genny to run the a/c it will be pretty noisy, inverter-generators aren't really any quieter than standard ones when running at or near full load. Your neighbors will love you for it (or at least not hate you as much) If you want you can bring a heavy duty extension cord and place the genny 50-100 feet away. Most of the noise come from the exhaust so point that out into the woods.
I start a camping trip with the fullest cylinder on the trailer and use the other one for the genny, placing it well away from the trailer. When the genny cylinder is empty I move the genny nearer the tongue and connect it to the cylinder on the trailer. Then next trip into town I swap the empty cylinder for a full one. When I return I put the full cylinder on the trailer and the one on the trailer goes out in the woods with the genny.
That way I have plenty of time before I run out of propane to make the tank swap while always having propane available to both the trailer and the genny. And I never have to swap a partially full cylinder to be sure I have enough.