I do not think you should let the kids play in the water. The river appears to me to be too fast and I did not see any calm areas.

The colorado riverway rund east from Moab or you can come from the east off of Interstate 70. You could do the drive as a day trip in about 3 hours from Moab to I-70 and then back to Moab. It is worth the time.

Yes, there are many camping areas along the river.

There are small campgrounds along the river, very bare bones, with pit toilets and I think a running water source. We stopped to use the toilet at one. As mentioned there are a couple really nice Dude Ranches up towards Castle Valley with lots of cabins and accomodations. I'm not sure under whose jurisdiction these campsites fall but no doubt the National Park Service or the National Forest Service, because it is a protected river. I would check with both of them for more information. You may also want to check with Dead Horse Point State Park which is in the area and overlooks Canyonlands National Park and the Colorado River. They have rustic campsites with great views. There is also an International Hostel in Moab, UT called the Lazy Lizard.