Re that link to the kit. That is your typical direct drive "1000w" 48v kit. Its not the fast 6t wind, (30mph) but the 7t wind that tops out at 278=-28 mpg.
This is what that motor can do. It can carry 300 pounds up long, and even steep hills. Like 8-10%. That 300 pounds is you, the bike, the motor, the battery, the trailer and the kids. I tested this motor to destruction for E-bikekit.com, and later became an employee there. Same type motor, and winding, but there are a zillion manufacturers of that same motor. At 300 pound load, it will climb 8% without slowing enough to cook the motor very fast. The way you know you are killing the motor, is if full throttle and your pedaling slows you below 12 mph. at 8-10 mph, you are on the way to melt down if your hill is too long. At 300 pounds, you can climb 6-8% grades at 13-15 mph. You can climb 8% for miles. for an hour or more. So I'm talking you can climb 2000 feet of vertical at 300 pounds. The motor will be hot at the top, but very unlikely you will melt one. Its quite hard to kill these motors with 48v, unless you overload them more.
I betcha your load is more like 400 pounds though, or even 450. This means your time to overheat shortens, very short if you slow to 8 mph with full throttle on it. So if you overload this motor, in 26" wheel, you will have about 30 min to get to the top of that hill.
I think you said the big hill is 2 miles? and only 200 feet? That is not steep, and a 1000w motor should do it. if you did slow to 8 mph, you'd be up it in 15 min. That will heat it up, but not melt it. Chances are, a hill that long that is only 200 feet gain, you will get up it in less than 15 min, and you will get up it at 12 mph or more.
Making the push trailer so you can use 20" wheel is a good idea, but more child trailers don't have the wheels in forks, and cannot use a hub motor easily.
But if that is all the hill you have, you will get up it with a big load of kids. If you get to the top and cant touch the hub without cooking your hand, then you should drill some holes in the covers. They won't cool the hub that much, but once hot, it will be allowed to cool quicker than if sealed, and by smell, you will be able to tell when you are pushing it too hard.
At 450 pounds, you maximum you could do is a hill about 500 feet vertical, in a mile.
I'm not guessing this shit, I did extensive testing of this type motor, so E-bikekit would be able to put sensible limitations on their warranty. Quickest I ever cooked one off was about 15 min, but that took 4000w. At 1000w, you generally always have 30 min to an hour before one melts. In fact, I never did actually melt one down on 48v. I just got them hotter than they should be getting, and stay in warranty.
Again, the load they can easily take goes up to 400 pounds in a 20" wheel. There are lots of adult size bikes with 20" wheels. Consider getting one of those for your pull trailer bike. The 20" wheel, if you have some gears, will help you with pedaling too, same cogs on the chain will be a lower gear. Something like this would be ideal.
