Are you going N-S or S-N? Are you using the main corridor trails i.e. Bright Angel/North Kaibab? How many miles/day do you plan to do? Just curious.
The difference between hiking with a day pack or no pack and a 40-50 pound pack is huge
I have done this trip twice but not in June. My biggest problem was postholing in the snow below the North Rim. It was a tough trip with a much lighter (24 pounds) pack in cool (March) weather. A 50 pound pack in June will be much harder. I hope you realize what you're attempting. This is quite an undertaking for someone who has never been out backpacking overnight before. A long walk after a night spent in a hotel is different than a long walk after spending the night sleeping on the ground, which will most likely be fitful if you have no experience in overnight backpacking.
You didn't ask any specific questions but I'll assume you posted because you're looking for advice. So here goes, in no particular order:
1)Try, try, try to get that pack weight down. You won't need a heavy sleeping bag. You can share many items like a stove, pots, tent, etc. Honestly, there is little reason for 3 people sharing equipment in warm weather to carry 50 pound packs, even with lots of water. You seem to have an open mind. I'll bet you're taking lots of stuff you really don't need. Learn to let go.
2) Soon, start training with a pack on. All 3 of you. On hills. Try to simulate the real McCoy. See my second paragraph again. A heavy pack on a long descent on a rocky trail is going to place tremendous stress on your feet. That stress cannot be simulated on a treadmill or in the gym.
3) If you don't use them already, look into hiking poles. Every pound of weight you put on them is one less pound on your feet. They really do make a difference.
4) Your treadmill training is on an incline. Good. Now try to train on a decline
as well. Studies have shown that more muscle damage occurs going downhill than uphill and you're facing a long, long descent with a pack on.
5) If at all possible, I strongly suggest a full "dress rehearsal" trip before you go. Use the same clothing, pack, shoes, everything you'll use in the GC. Even socks. All 3 of you. Try to simulate the distance and terrain although the latter will be tough in Florida. Go out for at least one night, two is better. Better to discover problems then than at the bottom of the Grand canyon in 100 degree heat. At least sleep out in your yard for a few nights.
6) How well do you know the other family? Are their capabilities similar to your party? They could become a liability to you.
7) I'll assume you have applied for the permits? The first day to apply for June was Feb. 1. Campground quotas fill up fast.
8) Read this
. You can learn lots from other people's mistakes.
9) You said you're prepared for the heat
but I hope you know that inner canyon average high temps for June are about 100 degrees. And that's just average. It could be hotter.
IMO the combination of distance, terrain, heat, pack weight and your experience level (let alone the other party's) could be a real recipe for trouble. I would take a hard look at what you're attempting.
Good luck and have fun. It's an incredible experience and I'll be there for another dose in April!!!