OK... Coach batteries won't hold a charge very long. Have to jump them for using generator. Then I have back AC for a while, and sometimes front kicks in, then stops. BTW its Been 92o for the past ...
When plugged into shore power for a few minutes, go measure the voltage across the chassis battery. You may or may not measure 13.8 volts.
If you do, disconnect shore power and measure again. If it's 10 volt or so, you have a bad battery. Replace.
If you do not, than you need a Trik-L-Start or similar device that'll keep your chassis (starting) battery topped off. Do not depend on the roof mounted solar panel as those are too small to do anything worthwhile.