I am not familiar with Dometic units, I have 2 Coleman units on my coach, controlled by a single tstat. If your tstat controls the unit thru a data wire vs the normal 12v Y1 wire, then interference could be the cause. I had pursued my issues for almost two months before I tracked the culprit to an ac to dc 12v wall transformer. Once I replaced the transformer units have been trouble free. I would start by turning off all your 120v breakers except for the main and the a/c unit. See if the unit will run normally. If it does, then I would begin turning on the other breakers one at a time, monitoring the unit. My issue was found when I turned on one of the general receptacle breakers on the inverter sub panel, which happened to control all my entertainment systems in the coach. The transformer powered my HDMI to CAT5 conversion module and was hard to locate. This may or may not be a solution for your system, but I would find the schematics for your tstat to see if it controls the unit thru a data wire.
Dan & Sharon (Kasey, Our Yorkie, RIP 9Jan'05-26Jul'17)
2012 Winnebago Journey 36M
2020 Chevy Equinox, Blue Ox Aventa II, Air Force One
If You Obey All The Rules, You Miss All The Fun