It depends on what the charger setup is. A lot of trailers in stock form are not going to give more than 10 or 15 amps max to the battery, the rated capacity has little relevance when there is a high voltage drop with those long undersized cables that save $50 at the manufacturer. Your current is determined by the difference between battery and charger voltage and when many chargers only supply 13.6 volts and your battery is going to be over 12 .... well you need *very* low resistance. Your quick charger may do better depending on capacity given the short leads and typically a higher voltage as well.
Disconnecting the battery depends on which type of external charger you have. Try it and see what the voltage is at the battery when starting from a low charge to get an idea, you may be appalled at how much the drop is on a stock setup. There are many threads on how to improve charging, but as most are a bit of work and an external charger is simple ask how often and how long you will be off grid.
