If your coach has the original type converter/charger, it is a single stage charger which is harder on the batteries than a new 3-stage charger. A couple of good multi-stage chargers are the
Iota DLS-75/IQ4 Smart Charger (or the DLS-90/IQ4 if you want 90 amps rather than 75 amps) or the Progressive Dynamics 9260 (60 amp). The higher amperage Progressive Dynamics are harder to find.
I just unplugged my old battery boiler and replaced my 1200 watt inverter with a ProSine 2000 watt inverter/charger that has a built in 105 amp multi-stage charger.
As Richard pointed out, if you leave your coach plugged in with the merge switch off, your chassis (engine) batteries will not charge. If you leave your merge switch in the on position, both banks will be charged. If you do leave the merge switch on most of the time, it is a good idea to follow Newell's recommendation to replace the merge relay annually. I rarely use the merge relay as I have a Trik-L-Start that puts 4-5 amps from the coach/house batteries into the chassis batteries as long as the coach batteries are being charged but will not allow the coach batteries to discharge the chassis batteries (diode protected).
Using an external battery charger will work as long as it is an automatic 3-stage charger. Otherwise Richard's warning should be followed. Replacing a set of batteries is an expensive lesson.