Good idea to plan ahead - and assuming you are driving from Texas - the first Q would probably be - how are you and your children at riding for long distances in a car?

The next would be what are you most interested in seeing? And that might also be something you discuss in part with the children.

I thnk one fairly direct trip would be from Texas up through New Mexico - including Sante Fe and Taos - and then up through the Chama mountains - over to the Grand Canyon, via Four Corners, Monument Valley, etc.

Or head up into Colorado and the many options there - and/or perhaps go to Moab, Utah (Arches National Park) and work your way down to Bryce/Zion, etc.

Whether you get as far as Las Vegas or say - Southern California - is all up to you and how many miles you and the kids can "enjoy".

We did a 6 week trip (!) when our kids were about those ages-- And it was before DVD players!!
A DVD will help, as will their Ipods--or Ipads. There is a lot of the west that is just traversed.
I think Tom's ideas are good--but maybe a bridge too far for the Grand Canyon. I think a loop up to Denver (lots to do there for kids for a couple of days IF you want).
Santa Fe and the Indian areas around it would be great.
I think Mesa Verde is a wonder of the world.
I'd suggest getting a map of the west and putting some pins in it--with the kids saying what THEY want to do. If they don't know about Mesa Verde, they should look it up and report to the family what is there.
Then--connect the dots.
I'd also ask what your vehicle is. For our long trip, we had a conversion van--and there was plenty of wiggle room!! Not necessary for you, but it will contribute to how long you can drive before needing an activity.
And I will sort of warn that while adults can endlessly look at hillsides of autumn trees change color and huge craggy mountains and red rock arches, kids, not so much!! They need some action words, in my opinion.

I note that your chosen states are west of Texas.
The National Parks and Monuments you could visit include White Sands, Grand Canyon (South Rim), Death Valley and Yosemite.
I would not try to stretch it past 4 major attractions.
The things in cities that would appeal to the kids would be the zip line under the light show on the Fremont Street Experience, the roller coaster at Buffalo Bills in Primm and maybe the Sandia Peak Tramway in the east end of Albuquerque.

You could go through northern New Mexico and then into Arizona along I40 visiting Petrified Forest, Meteor Crater, attractions around Flagstaff (Walnut Canyon, Sunset Crater, Wupatki National Mounument), Grand Canyon. Then go down to Sedona and the Verde Valley (Montezuma Castle and Well, Verde Valley Railroad). Down through Phoenix and I-10 to Tucson, Tombstone, Bisbee, Chiricahua National Monument and back trhourh Las Cruces and El Paso.

It seems to me that getting to California with stops at GC, etc. is going to take most of the 9 days, without a return!!

Where in Texas are you located? Anywhere in West Texas would make it a lot easier than if you're in the eastern part (Houston, for example). In this situation, starting point is pretty important - Houston to El Paso is over 10 hours, so if you do happen to live in the far eastern part, you'd use up 2 whole days just driving in/out of Texas.

Without knowing exactly where you're starting, I'd say the Colorado road trip is your best bet. Decent temps up in the mountains as compared to the heat of Arizona. Make a loop that goes through Carlsbad, NM so you can visit Carlsbad Caverns. If Texas is hot (and it probably will be) you can stop at Balmorhea State Park coming and going for a few hours.
http://www.tpwd.state.tx.us/state-parks/balmorhea

Loop through Colorado - Rocky Mountain National Park is always a good bet but you could also just go to southwest Colorado and include parts of NM. Can't go wrong either way.

Stops I would consider . .

Carlsbad Caverns

Grand CAnyon

Hoover Dam

I would not go as far north as Denver in such a relatively short time period.

I would head to Carlsbad, White Sands, up through ABQ [Tram ride is ok, but expensive for 5 and the drive up is nicer] then taking the Turquoise Trail up to Santa Fe. On to Taos, over to Durango and Mesa Verde. That would more than take up your time period. Lots to see and do along the way. Will be happy to provide specifics IF this interest you.

Denver is 9 hours from Carlsbad, Durango is 8. And Mesa Verde is 9.5 hours. Why not Denver??

And we don't even know where the OP is coming from yet, Texas is a huge state. Lubbock for example, is the same distance to Durango or Denver. Amarillo is actually closer to Denver than Durango. I just think it's a bit early to start ruling out destinations until we hear back from the OP on where they're starting from and what they're interested in.

Good catch/calculation.They need to decide what to see--and what is BETWEEN. AND it CAN be a LOOP--go north and come back south.
From Denver there is also CoSprings and the AirForce ACademy--and the great Sand Dunes before going across the bottom of the state.

I would do DebitNM's trip in a minute. In fact, I have. But with kids I would try to add one of the narrow gauge railways, either Chama or Durango, both if possible.

Mesa Verde is a must. Acoma on the way back is worth a long detour.

Two things if you do Carlsbad. If your kids are adventruous, consider the Wild Cave Tour. There are two different tour. They allow only 8 people on Saturday to do one tour and then 8 people on Sunday to do the other tour. Make reservations as soon as they are available(6 months in advance, I think). Only an hour away from Carlsbad is a little known National Park, Quadalupe. You might as well hike Guadalupe Peak-It's the highest point in Texas.

I would then vote for you to head up to Mesa Verde and Moab/Arches. www.deserthighlights.com-again if your kids are adventurous. Very safe company and outstanding.

If you see more than 2 or 3 parks, you might consider getting a National Park Pass(it's good for all parks, monument, rivers, etc for a year $80)

If you head towards Grand Canyon, you should do Petrified Forest. You can do each of these parks in a day.

It would actually be a good time of year to camp, most places. I like to camp, my wife and daughter don't like it nearly as much as I do-so it isn't for everyone.

IF you take the narrow rail in Durango, only do it one way; take the bus the other way. And truthfully, I am not sure how much the kids would enjoy it. My son went with me on the Chama one when he was 14 and was pretty bored with it, except for when there was a herd of cows on the tracks and we had to wait for the wrangler to come and get them off.

If you go to Mesa Verde, make reservations at the lodge (Far View) IN the park--as soon as possible.

The really cool thing to do on the Durango trail is www.soaringcolorado.com It is very expensive though.