If it was just lights I'd say Converter, but with it also affecting the AC ala a brown out ... That's odd. Sounds like a connection developing resistance as it heats up. ATS going bad? Plug connection into RV going bad? An issue with the campground pedestal? You might want to (carefully) take voltage readings at various points in the system to try to determine where the voltage drop is happening.
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2021 Thor Four Winds 26B on Chevy 4500
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