Tow/Haul button: what is it for?

As others said, it alters the programming of the transmission controls to work better with heavy loads. Since a motorhome is always a heavy load, I would leave it engaged all the time. (I say "I would" because my motorhome is old enough to lack the tow/haul mode.)

Besides the shift points themselves, it tends to make the torque converter lock up more readily (I think) and may alter some of the details of the timing of the actual shifts in an effort to keep the transmission operating temperatures down.