Lithium battery capacity to last 3 days running all the high draw appliances will cost you more than the trailer.
Yes, batteries get recharged automatically when connected to the campground power utilities.
The answer to your conundrum is a generator consuming petroleum carbons if you are not seeking solar as the source of power to recharge the batteries while boondocking.
"Good judgement comes from experience. Experience comes from bad judgement."
Air #48582, S/SO #003, WBCCI #4584