My personal solution to this is to avoid have two armies commanded by Generals anywhere near each other and always make the attack move with the army that has the General.
In your specific example, I would actually have sent the Govenor of a holiday well away from the battle before I attacked. That way even if his troops turn out for the fight at least he doesn't.
Where two armies both with generals are operating together, I always move both generals into the same army before making my attack with that army.
This still leaves a problem when the AI initiates the action and i have found myself cast in the role of Captain when the AI controls my General which is really annoying.
Some choice on the pre-battle screen which allows the player to choose which army they command and whether the reinforcements are included or not would be preferable.
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