Would your family be interested in something like this?
http://www.thetrain.com/train/
There are also hotel packages that include staying at the Grand Canyon Railway Hotel in Williams (near Flagstaff), Arizona and a hotel inside the GC National Park, depending upon the package you choose. It also includes some meals and a narrated bus tour. Friends of ours took their family on this a couple of years ago and enjoyed it.
Have fun! The Grand Canyon is definitely worth visiting!
We are staying at the Grand Canyon Railway Resort right now and i can confirm your advice--this is a neat place. We are staying in the RV park adjacent to the hotel, but we are allowed access to all the hotel amenities(indoor pool, hot tub,restaurant, on-site kennel). They have several packages available which make the trip affordable.
The train ride is a lot of fun. My kids are 14 & 12, but the 12yo is mentally handicapped, more like a 1-2yo. He enjoyed the wild west show before the train departed as well as the cowboys who wander the train with their guitars, singing cowboy songs. The ride is about 2hrs long and we saw some antelope right outside our window. They give you about 3hrs in the Canyon, or you can make arrangements to stay overnight in the park and come back on the train the next day. From an adult point of view, 3hrs is not a lot of time. From a child's point of view, it was plenty. You can eat in the restaurants there, but we decided to take our own picnic. We sat under a tree and ate, gazing at the canyon all the while. My son couldn't take his eyes off it. We do not hike due to DS & DH disabilities, but we walked along the rim until they were both tired and breathless. On the way home the train car was very quiet. A combination of sun, high altitude, and activity worked its magic on the kids. As you near the end of the train ride watch out for "bad guys". They board the train and rob everyone. It was great fun and even my oh-so-cool 14yo got into it. When you get back to the hotel you can go eat supper at the restaurant, Max & Thelma's. They have a great buffet or you can order from the menu.
Everyone tried to talk us out of taking this trip--DH would need oxygen(he did), DS would be too tired(he was), it would be too hot(it was 85 degrees), too crowded(nothing like WDW!) But it was worth every bit of difficulty. In three hours, the canyon colors change a lot. If we could go without the kids, DH & I would definitely stay over and take it all in. With the kids, probably not. But your family may feel differently. My one piece of advice: hold hands. The rim has a low stone guardrail, but it would be easy to fall off. We saw several adults and a few kids climbing over the rails to get pictures or just to look over the edge.

We had a strict rule of no running and no horsing around.
I hope you go and have a great time!