One week is enough.....
If you go for one week, every year, for the rest of your life.
My advice for when you go. Focus on just a few places each trip. Maybe for your first trip, you could drop your trailer off, and do a marathon drive, just to get a feel for things and where you might like to spend some time.
Research the daytime and nighttime temperatures. At the perfect time of year it can be 95 degrees during the day, but 15 minutes after the sun goes down, it could be 45 degrees. And as Streamahead mentioned, elevation plays a huge part in the temperatures and comfort levels.
We did our hiking and driving from 5 - 9 am and pm. You should plan to do SOME hiking even if you aren't hikers. You simply can not see the coolest stuff from inside your vehicle. That being said, the journey to any destination in the southwest, is spectacular, even if you just drive by. Bryce and Arches are great for short hikes. ALWAYS have a gallon of water on your person. If you set a plastic water container down, consider it given to critters.