Ok, we have two sides, why cant both be right? I am getting a sense that the battery is not keeping a charge. If the alternator is working properly, it will charge the battery at idle speed. If it is not working properly it will not charge adequately and may work properly when the engine is at a higher rpm. An alternator diagnotsic MAY determine this to be either way. If a diagnostic results in a good operating alternator and charging system components, then move to the battery as a week link in the process. Don’t bicker any more on this one, fix it and move on.