[Desert185]

What John said.

The truck's trailer connection is like a trickle charge that would take an impractical amount of time to recharge the trailer batteries to an acceptable level they need to be. Run the generator twice a day instead, and keep the batteries charged rather than running them flat. They'll last a lot longer keeping them charged above the 50% level.

One thing I carry that helps in an emergency situation is a micro jump starter, which would work well for starting your generator if it's battery is flat. Costco carries them for $50-$60, and of course, they are all over Amazon.

Edit: My trailer plug is hot all the time. The truck doesn't need to be running or the ignition switch on to provide 12V power to the trailer. I always disconnect it if spending a night while hitched, although, with two, good truck batteries they won't go flat overnight. Something to confirm, as not all systems are the same.