I'm going to recommend something different: The NORTH RIM.
My family visited the North Rim over July 4, and it was incredible. It's much less crowded than the South Rim, and it's a little cooler too. Because we were there over the 4th, every cabin was full -- probably much of the campground too -- and it felt "full" but not really crowded. Unlike the South Rim, you 're allowed to drive your own car around, and you won't have the parking problems that you'd have at the South Rim. You can get a mule ride, even if you haven't made a reservation, and they have a fun evening cookout.
The Grand Canyon Lodge itself is quite incredible. Built of stone right into the hillside, the lodge is dark, historic, and just plain beautiful. It contains nice restaurant, a reasonably-priced deli (large pizza for $17, hot dogs for $2, etc), a bar, and a gift shop. It also contains a lovely sitting room and large stone terraces overlooking the canyon. Be sure to go into the "basement" moon room; it's nice too. Steps from the lodge is a small museum and another gift shop.
Every evening around sunset people begin to congregate on the two terraces, and wait staff comes around selling adult beverages. Because it's chilly -- even in July -- the staff lights a fire in the GIANT fireplace, and people sit out for a long time.
On the 4th, they held a parade, which was quite the highlight for my kids. They brought out about 20 industrial-sized trash cans, bungee corded them together, and filled them with water. They put out water guns and super soakers, and every one began a massive water fight. 30 minutes later, the parade began. Notice I didn't say the water fight stopped; instead, people in the parade -- rangers, maintenance folks, mule wranglers, etc. -- were armed and shot back at the crowd. There was no saying which group "won" the water battle, but my girls were beyond thrilled with the event.
Like all national parks, you'll find wonderful ranger-led programs -- most of them free -- and a great junior ranger program.
The cabins at the North Rim look like little Lincoln Log huts. Very cute! We had a mid-range cabin, which was called a Pioneer Cabin. These are two rooms joined by a bathroom. My husband and I had a queen-sized bed (very good bed, actually), a bench, and a refrigerator in our room; our girls had a slightly larger room with a set of very sturdy bunks and a futon. Their room also contained a sink and a writing desk. The girls announced that their room "owns" -- I think that was good. The bathroom was small but functional, and contained only a shower, no tub. Ample towels, good water pressure. Maid service was prompt, even though they dragged clean sheets and cleaning supplies in big carts. No TV, no air conditioning, though the temperature was quite comfortable in the dark, cool cabins, and during the night I was even glad for the blanket (again, we visited July 4).
The park also has newer, nicer cabins called Western Cabins, which have porches and fireplaces. I would've liked to have had one've those rooms, but they were all ONE ROOM cabins, and with two teens, privacy trumps luxury. The park also has very basic, rustic cabins called Frontier Cabins; I know nothing about them.
One thing I would not do again is pay extra for a rim-side Pioneer. Yes, our cabin WAS right on the rim. It was also as far as possible from the parking lot, and it was straight downhill! Getting our cooler and snacky foods there wasn't exactly easy. This would've been worthwhile IF we'd had a nice porch on which to sit and take in the view, but we didn't. The view was blocked by trees. If I went back with just my husband, I"d love to have one of the rim-side Western cabins, and I would sit for hours on the porch overlooking the canyon. But if I go back again and want a two-room Pioneer cabin, I'll try to get a LOW NUMBERED cabin because those are closer to the lodge. On the positive side, our cabin was incredibly private.
The North Rim is close to NOTHING. You go there for the quiet solitude, the lovely views, the wildlife, and the park itself. It is not reasonable to think you can drive out of the park for a quick lunch; going to eat outside the park would likely be a two-hour round-trip drive. Once you're in the park, plan to stay there. You also won't have internet or phone service inside the park.
I'd say that a 2-3 night stay at the North Rim would be PERFECT. That's just enough time to get yourself settled, ride mules one day, hike one day, enjoy the evening cookout, and just relax as a family. With your family's configuration, I would suggest that you try to snag one of the prime rim-view Western cabins for your parents (so you can all enjoy the lovely porch with the fantastic view), and get a two-room Pioneer for yourself and the kids. Though the two-room Pioneer does sleep six, I could not recommend six people sharing that tiny bathroom.
One negative: While we were there, a large tour group from ElderHostel took up many of the cabins, and they were among the rudest, most me-first tourists I've ever seen. Loud, crude, and determined to ignore everyone else in the park, they are not the typical friendly types you usually meet in the national parks. At the worst, I saw a HUGE group of them, including plenty of adults old enough to have better manners, push in front of a woman in a wheelchair who'd been waiting her turn to ride the train to the cookout. I hope never to encounter their like again.