A temperature swing problem comes from two things:
1. Location of the sensor(s)
2. A built in "swing" threshold of more than plus/minus one degree
Most RV t-stats won't call for more cooling until the temperature changes by more than one degree, which gives a slightly more than two degree total swing. Coupled with typical RV sensor location(s), this is often uncomfortable. Sometimes fixing the location is easier and more effective than changing the t-stat.
If mounted on an exterior wall, try insulating the t-stat from the wall with a piece of 1" thick foam board. Also check for air currents around it - too often the t-stat is cooled/heated by air currents from a nearby duct, stovetop, etc.
What year Dynasty is it? And what model Dometics a/c (or heat pump)? That can make a difference if you want to substitute a different t-stat.
Former owner of 2004 American Tradition and several other RVs
Home is in the Ocala Nat'l Forest near Ocala, FL