First, No, I know of no Coach power systems or controls that will affect the engine or the engine battery. But, yes, your power stairs, your power awning, and your exterior lights are powered by your engine electrical system.
But, from my experiences with engine systems, if your alternator/regulator are not operating properly, you would get the symptoms you mention. But a competent Rv mechanic should have checked this first.
And considering you have already replaced the engine battery, I still go back to your Alternator/regulator as the most likely cause of your problem.