I'm not so sure if the tow button works in manual mode, because I've never tried it.
I use manual mode for all towing and hauling. Even when I'm not towing, like big hills with a 45 mph speed limit, I use it. It's all about keeping the torque converter temps under control. The higher gears cause more slippage, which generates more heat.
Putting it in manual shift mode, totally negates tow mode. Personally, I use tow mode for freeway on-ramps when unhooked and for residential/surface street towing in town, between 10-35mph. I've found that with over 1200# on my trailer in drive, driving from one stoplight to the next, it hits third Way too fast, bogs, then hits second, and then third again. If I have tow mode on, it just shifts smooth and sequential. If my load alone gets over 3500#, then it's manual mode all the way. If I'm on hills, I use manual even under light load. As an example, today i drove 70 miles on hwy 50 with about 2900# behind me. That strip of hwy is 65mph, and known for long uphill and downhill stretches. If I go in drive, the tranny gets hot. It will downshift all the way to third just on cruise control at 60, but i'll run in the last third of the temp gauge, touching the 'red' several times. What I do is set my cruise at 60, and hit manual (4th). When I get close to a good climb, i toggle 3rd, and it takes me up with no issue. Same thing for the descents, I grab third, and I won't coast over the speed limit. RPMs don't get over 3k, but the tranny temp never even reaches the halfway point. Now the hills aren't all that steep here, just long. When running the divide on I-70, I've many times run 70MPH in 2nd on long descents and climbs, pulling up to 5200rpm. While I wouldn't advise revving that high for that long, I have done it, quite a bit, and had no engine issues. Maybe it stems from being a truck driver, but my go-to for controlling speed has always been gears first, save the brakes for emergencies.