Start with the easiest solution first... Check the circuit breakers. (both the house and at the units) there are separate ones for the controls and for the operations of the compressors (the controls are usually operated on 12 volts the compressors are 120V).
It sounds like your A/Cs are getting control power, but not power enough to run the compressor(s) after those are clear, check the connections in the junction box under the ceiling panel. (The spade connectors)
Side story, but related:
During a trip though New York a few years back, it was so hot, (101 degrees) I had the generator running and both roof tops powered on (along with the dash A/C at max!) it was just enough to keep the coach cool enough to keep the dogs from heat exhaustion (and, we were still sweating...) Once we had cleared the GW Bridge (3 hours of stop and go... mostly stop...) we were heading up I-684 (very poor condition and very bumpy) My front Dometic A/C unit kept dropping power and shutting down then trying to power back on with the next bump... It finally burnt out the compressor!
When I called the Camper repair (replace) store, I went looking for the model and serial numbers and when I got into the junction box I found the blue wire (with a spade connector clip) was so loose, there was no resistance to pull it off. (I fiddled with it once I were connected to shore power and even though the compressor was burned out at this point, it was still trying to start... (I wasn't pulling the connector off, I was jiggling it in place and it was losing connection, even though it looked connected... That blue wire, (a number 12wire) carried the power to the 120v breaker...
Maybe this will help...
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