Your tow vehicle should be able to handle 120W of load out that pin, its probably fused for like 30A.. it just wont charge a battery very well with voltage drop alone.. A static load of Watts, will pull more amps as the voltage goes down.. so if its getting 12.2V in your trailer at 10A, your turning that into a usable 14.6v charge and outputting 8A.. otherwise that same voltage drop would never charge a battery up.. but it would run a 10A static load just dandy at that voltage.. this is why a direct connection to alternator w/no booster requires such absurdly large wiring, cant have a 10th of a volt drop let alone a whole volt.
Trailer Brakes are wired through that plug, they pull far more amps than this DC charger will.. check your fusing but you should be fine.
I've got a Victron BMV-712 wired up to my battery in the trailer, through my factory plug I only get ~4A charge input.. a full 7h trip on the road barely put a few AH back in with the fridge also fighting for that power while driving down a hot interstate.. its adequate enough to maintain the charge I left with in the summer, but not much more.. If I leave home w/a full charge I get to camp with a full charge, no matter how far I go.. but if I leave camp w/a flat battery the factory wiring w/out a DC charger is not going to do anything but keep the fridge running.. this is why I added a 325W fixed solar panel on the roof, now I see my battery getting 15-22A going down the highways in good weather.