the first thing you should have done before storing it, was to install a battery disconnect switch.
i have one and i simply disconnect the battery and it stays charged, unplugged, for months.
your trailer's converter will recharge the battery just as well as most standalone battery chargers. you would have to drive for hours to get your tow vehicle to recharge a drained battery. more than only 5 hours.
if you don't have solar or shore power, the only way to recharge a depleted battery, is to have a generator. you just plug the shore cord into the generator and let it recharge the battery.
we dry camp almost all the time. i have two deep cycle batteries and a Honda 2000 and we can go 4-5 days without a recharge. even with the more power hungry HTT that we have.
and Zoe the Wonder Dog(R.I.P.)
'07 Roo 23SS pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC