It can get complicated, but serious thought now will save you from costly mistakes.
We are already into August. Surely by September the weather will moderate. Can you park the rabbit tractor in the shade and just let them stay in it for the next month or two? They may run out of grass, but it is easy enough to pick weeds etc. and take them to the rabbits.
You referred to them as babies, but didn't tell us their age. As rabbits approach the three month mark, you will likely want to be careful that the young does do not become pregnant too soon. You may need to separate the buck, preferably to a next-door position so they stay "friends".
The spot in the shade sounds promising, but how far is it from your source of water? Carrying feed is one thing, but carrying water any distance gets old very quickly. Especially in winter, when water has to be changed often enough that they can drink. There are ways to keep the water from freezing but they require electricity . . . so think long and hard about where you should situate your rabbitry.
Some points to consider:
1. The wire you choose for the rabbitry is very important. Mink, weasels and rats can get through anything larger than 1" x 1". Chicken wire is no deterrent to animals getting in or rabbits getting out. It can be chewed through easily.
2. Bird netting will keep out birds, but neither it nor a tarp will prevent climbing predators like raccoons from going over the top and killing the rabbits. Raccoons are also very good about reaching through wire and nabbing a rabbit, eating it through the wire. I had a broody pen once made of sturdy wire shelving sections, 3/4" apart. One hot moonlit night, a raccoon reached through, grabbed a chick and did just that. I heard the broody screaming and ran down but it was too late for the chick. I did a quick fix to contain the broody and remaining chicks until morning, but darned if the raccoon didn't come back to finish pulling the chick through the bars and eating it.
3. Rabbits will dig if you let them. Sometimes they will dig their way right out. I think above-ground nest tunnels or covered boxes are a better bet and I think using paving stones to floor the colony is a good idea.
4. A solid roof is a very good idea. It needn't be fancy (think used materials from the re-store or Kijiji) but it not only gives protection from the weather but also from predators. Last year we were able to get used steel roofing from a closed mink farm at about $8 a sheet. Score!
Give it all some thought and we can discuss it more later one.