If you are just trying to make time, use I-80 to I-76 to get to Denver. Since you have never been to Colorado, I would suggest spending a couple of nights in the Denver area. And I would recommend that you stay at Chatfield Lake State Park campground (full hookups) while you are here. You will be located on the southwest side of town and within easy freeway driving distance of tourist attractions like Buffalo Bill's Grave and Museum and the Coors Brewery.
From there, you can easily head southwest on US 285 into the mountains to Salida. If the weather is still warm, you might want to take a raft trip through Brown's Canyon or go fly fishing in the Gold Medal trout waters of Bighorn Canyon on the Arkansas River.
Then take US 50 over Monarch Pass to Black Canyon of the Gunnison NM (you likely won't have any problem with a campsite there in mid-September). From there, continue on US 50 into Montrose and turn south on US 550. If you have a couple of nights to stay, try Ridgway State Park for camping and just take your truck south to Ouray and the Million Dollar Highway to Silverton for a drive through the spectacular San Juan Mountains. I would not take your trailer to Silverton!
At the town of Ridgway, take CO 62 to Placerville, being sure to stop on Dallas Divide before you get to Placerville to get photos of Mt. Sneffels and the San Juans. From there, take CO 145 to Norwood and Naturita, then CO 90 to Paradox and US 191 in Utah. Turn north to Moab and enjoy your stay at Arches, Canyonlands, Deadhorse Point, Capital Reef, Bryce, Zion, and the Grand Canyon.
You will have then have seen a narrow slice of the real Colorado--eastern plains, urban sprawl, Rocky Mountains, Colorado Plateau, irrigated farms, ski resorts, silver mining towns, cattle ranches, and the most isolated valley in the state (Paradox Valley--home of the oldest uranium mines in the nation). And you will have traveled a route entirely free of Interstate highways once you reached Denver. Of course, I'm not sure how you are going to do all that in 2 weeks!