My buddy upgraded his wiring to #8 wire, and reported that his trailer battery will now fill up while towing from one location to another as long as he drives about 3 hours or a little more.
But because he wanted to stay put longer at a lakeside campground, he ended up buying a small generator and charges the battery with it. A solar panel probably would be a better idea.
If you install a pair of 120 - 150 watt panels on the RV roof, you should not have a problem with arriving with low batteries.
SunElec.oom had 140 watt solar panels for $229 a few months ago. THey are 12 volt nominal (21 open circuit - what you want) and aluminum frames for attaching to the RV.
There are less expensive per watt panels without frames, but you don't want that one.
Some say to run a larger cord along with the factory 7 pin wiring. By installing a #10 wire, and a special plug, such as 277 volt angled plug (so your brother in law does not plug it into house power because it fits and blows up a battery). This connection is larger and can carry 25 amps with minimal voltage drop.
The 7 pin has really small wires, perhaps #12, but likely smaller #14. And you need the ground wire to handle not only the battery charge 20 amps, but also the brakes 15- 18 amps, and all the running light amps as well. Sure some of the ground amperage might be carried through the hitch to the truck frame.
If you buy some #10-3 wire from Home Depot, and run it from the battery to the truckbed, to a plug there, then #8 wire from the alternator to the relay that will shut off when the engine is off, then to the plug at the back of the truck, you will have maximum voltage to that plug while driving.
Good luck,
Fred.