We've just come back from a tour of the South West and felt we had just skimmed the surface. The Grand Canyon Village (South Rim) is a long way from anywhere, so if your kids aren't happy spending a lot of time in the car... That area has so much to offer, but you have got to love walking and scenery to get the best out of it. There's lots of outdoorsy things to do, but as with everything, there're quite pricey and with a family the dollars really start to add up.
Just to give you an idea of what we did and what we would have done differently (obviously with kids you will be looking at things in another way):
Night one and two-Vegas
Walked everywhere along the Strip (I'd avoid anywhere you see people lined up along the sidewalk as they're selling the kind of merchandise you don't want your kids asking questions about). While not the first place you'd think of with kids, there's actually quite a lot to amuse them, especially if they like thrill rides. This is a place you can spend a little or a lot, no point listing the attractions (you can easily do this yourself) but I don't think there are many places in the world like Vegas and if you're "in the area" you should consider a visit.
Night three and four-Grand Canyon
Passed the Hoover Dam en route to GC (didn't stop but if you have an interest, this is a good way to visit).
We worked out that the trip should take about 4 and half to 5 hours, but you forget that just getting the car and familiarising yourself with it takes time, and traffic around the Hoover Dam is pretty slow, and so on, so in the end it took about 7 hours from hotel to hotel including a stop for lunch.
We stayed in the Village and were so glad that we did - getting up and only having a five minute walk to see sunrise over the GC was amazing. One thing I would mention is that you said you plan to travel in summer - be prepared for really fierce heat, especially if you intend to go down into the canyon (walk, mule, etc). Definitely see the Imax film, and if you can manage a flight you'll not regret it. Two days is in my opinion the bare minimum, and if I could do it again I'd spend maybe four.
Night five - Monument Valley
Our drive the next morning included lots of stops along the Rim for photo opportunities and a brief visit to the Tusayan Ruins - and we arrived at dusk at Gouldings Lodge in Monument Valley. Despite loads of warnings about the condition of the drive around the Valley, we found it okay as long as you take it slow and we only had a compact car. There are official tours which can take you to parts of the park restricted to Navajo guides, and the little vehicles they use are open, so you can get great pictures all the time. The only negative there would be crowds, and if windy, you get a lot of red dust. You could spend longer here but I found one day enough.
Next stop was Page (Night six). A strange little town (apparently the most remote community in US), but kind of interesting too. I would not recommend the calzone pizza at Strombolli's, it seems to be loved by locals but it bears little resemblance to any calzone I've ever had - maybe just a matter of taste! Visited the Lake Powell Resort area at Wahweap, but think you would need to be a water sports enthusiast to want to spend more than an hour or so here (views lovely but little else to do). Loved Horseshoe Bend which is a few miles out of town not sure whether I'd want to take small children or strong willed teenagers though, as the edges just make you want to peer over and the rock is soft.
Night seven- Bryce Canyon
Wonderful place to walk around, the pictures tell the story really, but one night is all you need (I think).
Night eight - Zion
I would have liked at least one more night here - beautiful varied scenery to drive through, be driven through and walk through. All the National Parks have ranger programs which can be great for all but especially kids.
Night nine - Las Vegas
Another long drive, much of this was scenic, but the last part was built up and traffic increased significantly. No problem if you're used to freeway driving, but after a number of days driving through wonderfully varied scenery with little company, it was a shock to the system.
This wasn't exactly a loop drive, as Monument Valley and Bryce required some driving over the same roads, but for the most part we were travelling new roads each day and never got bored with the scenery. The down side was living out of a suitcase, and again with kids this could be a problem (especially as mom will probably end up doing all the packing/unpacking).
If you prefer to be based in one place for the whole trip, Vegas or somewhere nearby (cheaper) could be a better option. There's so much to do and see in the surrounding area (Red Rock Canyon, Death Valley, Lake Mead etc) and then you could either take a mini break to the Grand Canyon or make it a holiday of two halves.
If you plan to do the Colorado River Float, make sure you book it ahead of time - we didn't (in October) and it was fully booked (arrggh). The bus goes from Page (the further away from Page your pick-up point, the more time you will be spending on a bus).
If you're anything like me you will end up with an itinerary that bears no resemblance to the original plan, but whatever you decide to do, you'll have a wonderful time in this area. My only real problem was the food, not so much the quality, but the temperature! Even food that came covered with a metal platter cover was only just lukewarm. But things like that are eclipsed by the natural grandeur of the whole area.
If you have any particular questions, I'd be happy to answer if I can, but my experiences may not be much use to you as we were a couple and Fall is less busy.