...and if you are really lucky...a 4th stage called equalization...either manual or timed...to keep the battery from sulfating.
That said....I agree with your mechanic. Batteries don't NEED to be left on a charger full time and only bad things can happen if something goes wrong with the charger or a cell in the batteries. Suggest:
1. Fully charge the battery to 100%
2. Buy a battery cut off switch at wal mart and use it on your negative battery terminal.
Don't plug the coach in...just turn the switch off. Do this on both chassis and house battery.
3. Come back as long as 2 months later and recharge the batteries from the passive loss that will occur (20-30% typical) ...This will FULLY exercise the batteries as you should go through all 3 stages of charging. Check the water....distilled only.
Rinse and repeat.