Looking at a map and rethinking, Channing is probably about 30 minutes from Dumas.
I wouldn't go to Dumas unless you were meeting some of your friends and family there. It just adds unnecessary miles.
Channing is about 55 miles from Amarillo. Go through Amarillo on I-40, exit on Soncy Road. Go north on Soncy and look for the FM 1061 / Boys Ranch Road exit. Take FM 1061 until it intersects with US385, turn right (north) on 385 about 12 miles to Channing.
Eat and fill with gas in Amarillo. Channing is a tiny little dying town, maybe 400 people. It's claim to fame was as the headquarters of the famous XIT ranch.
Allow about an hour from Amarillo to Channing, the road is a bit twisty, but the scenery as it goes through the breaks of the Canadian River is interesting. We hope it rains before June so it will be green.
If you are into history, you can stop at Boys Ranch, a community/school for troubled youth. It is located on the site of Tascosa, an early Panhandle town. There is a small museum in the old Oldham County Courthouse.
Tascosa was one of the few authentic Old West towns in the Panhandle, with saloons, shootouts, and a Boot Hill. It was visited by Bat Masterson, Billy the Kid and Temple Lea Houston (son of Sam Houston, Texas A&M class of 1878 or so).
I seriously recommend Palo Duro Canyon and the PPHM.
http://www.palodurocanyon.com/http://www.panhandleplains.org/Allow 90 minutes from Canyon to Channing, though you could probably make it in 70 if you really pushed it.
The PD Canyon is about 20-25 minutes from Amarillo off 287. Allow about 30 minutes to drive to the first overlook and take a quick glance and leave. An hour to drive down into the Canyon, and probably two hours to take a good look, picnic or hike.
You would have to get very lucky to get reservations, but a very cool place to stay at the park is the CCC cabins on the rim:
http://www.palodurocanyon.com/info.phpThe Museum is one of the best regional museums in the country. Allow an hour for a quick dash through, two to take a good look.
Amarillo is a town of over 230,000, so it has all the usual shopping, hotels, restaurants, etc. Let me know if you need any other suggestions.