I'm guessing that the battery
is fairly new. If not, some of the following may not be all of the answers you need.
You said "Batteries", is there more than one in the trailer?
If you are trying to charge 3 batteries, (1+2) unless you have a heavy duty alternator in your TV, as well as real heavy charging line to the trailer, you may not be able to bring those batteries up to full charge in about a 5-6 hour drive (if ever, see below)
Perhaps more critical than the output of your TV alternator is the size of the wires running to your trailer from the TV. The funny things that happens with TV charging are:
As there will be some voltage drop in the wire running from the front of the TV to the trailer's battery
, this will reduce the charging current passing into the battery and, if the drop is enough due to bad connections or undersize wire, it can prevent the trailers battery from ever getting a full charge.
The TV's charging system will see all of the batteries (TV & trailer) as one large battery and, as the TV battery voltage rises rapidly, it can cut back on the charging rate before all of the batteries are fully charged.
built in a Converter/charger designed to support the battery load and I would allow at least three days for that system to bring everything up to full charge.
I typically leave my Progressive Dynamics PD-4045 equipped system plugged in 24/7 so that it's 3 stage charger can properly charge and desulfate the battery, so it's always at 100%. (Yes, that was a blatant plug for PD-4045's)