Forgot to mention our 9 yr. old daughter and small dog are in group

You can't do much with a dog. Especially in Yellowstone. Bear might even break in car for that.

It would be wise to leave the dog near home with a dogsitter.
http://www.nps.gov/yell/planyourvisit/pets.htm
Are you coming from NYC or somewhere farther west?
What is the total length of your trip? Are you returning to New York or going farther west than Yellowstone?

It's going to take 3 days of driving to just "get there". I don't think Yellowstone is a possibility.
You can go through St. Louis and see the Arch.

Are you driving?

There is a reason why most of your route is called "the flyover states." There are of course things to see along the way, especially if you don't just take I-80 all the way, but there is a lot of corn and soybeans, and it is three FULL days of driving. Yellowstone is w-a-y past Colorado and would add another couple of days of driving and about 1000 miles.

What about looking for cheap flights and car rentals on Priceline? Get there in one day. Maybe take the Zephyr scenic train to Salt Lake City and fly home from there. Or get a one way car rental to Albuquerque and fly home from there.

I love driving and looking out the window, but this is a l-o-n-g trip for most people on the East Coast.

My wife and I have taken this drive several times. We are from NY also. Yellowstone is pretty much out of the question with only 6 days of travel time this doesn't mean its not possible if you want to drive nonstop without any sleep time and by the time you get to Yellowstone you will be shot. We have done this it's alot like work. There is not much to see until you get to Colorado.

Thanks for all the comments , I have ruled out Yellowstone .I am now leaning towards driving I90 (cooler)and have 4 days to reach Colorado Springs....any suggestions of attractions etc. along this route?

I did a similar drive 4 years ago with DS and 2 largish dogs when we moved house. It took us 4 days from MA to Denver. I drove anything between 450-550 miles a day, the longest I felt I could safely drive without becoming too tired. The route we took was I90, I80, I76s and I25s. AAA planned the route for us, and also arranged dog friendly accomodation for us along the route.
We couldn't really stop at any attractions because of the dogs, but we did take a break at Gothenburg, Nebraska along Rt I80, because we saw a road sign to a Pony Express museum and thought it might be interesting. It was in a park in town, and although small, it was worth the time. I did see a sign for Leonberger baskets somewhere along I80, but didn't have the time and also saw signs for Cedar Point, which I did want to see, but again didn't have time for.

It isn't going to be that much cooler, and it is further north. AT LEAST, see the ARch.
If your 9 year old still has any interest in dinosaurs, go to Woodland Park outside COsprings to the excellent museum there.

The sunflower fields in Kansas are worth a look--see how they turn their heads to the sun. Wonderful.
Just go ahead and "get there" and enjoy. And tell your child how bloomin' BIG this country is. It is a lesson in itself.

I will also say that having driven it a number of times, driving 500 miles a day is very conservative. The roads are uncrowded, speed limits are high, and you also gain time going west by time change.
I usually drive about 700 miles per day. Granted I don't have a child with me, but the driving is just what it is--steady and straight. Go for the goal of getting there. audio tapes are great.

If you plan take I-90 all the way west to see the SD Badlands, you can take US 16/18 and Wyo 270 to get to Guernsey in Wyoming (close to I-25). And see the Oregon Trail Ruts state park before you get back on I-25 south.
http://www.nps.gov/oreg/planyourvisit/site7.htm