First off it's impossible to overcharge your trailer
battery from the charge line. When was the last time your cranking battery was "over charged"? The safest way to charge the house battery while under tow is with the charge line from the tow vehicle.
If your
Scamp has a "converter" it already has a battery charger. If don't have a converter then a simple maintainer will work just fine.
If you're going to connected to 120 most of the time no need to worry about charging the battery at all since the converter should take care of your 12 volt needs.
Boondocking then other methods like a
solar panel work great.