Thanks all for the suggestions. I appreciate all of the positive "do it" support. In today's era, finding a week of time between kids activities is hard enough, so getting three weeks is practically an impossibility. It may not be the ideal amount of time to do something this epic, but it is probably as good as we will ever get.
I am looking at probably dropping the Grand Caynon in order to allot more time to the rest of the trip. As much as I really want to get that experience (never been myself even though I lived in Vegas for four years) I just don't think this would be the right trip to try to do it. I am coming to this conclusion because it looks like the park is only open for the day right now anyway and because we have the babies, we won't be in the position to do much more than take pictures from the rim. Doing any sort of hiking will be out of the question. Additionally, because we would be going in the summer and our older girls would be relegated to our converted cargo trailer, they would be enduring the heat which they won't be too happy with. It is also a park that is close enough to us that we probably could pick up on a week long vacation.
So now we might actually put Yosemite back in and then head North up 395 then cutting east towards the Grand Tetons. Any good scenic routes to take from Reno to Jacksonville?