Troops in defensive posture will only attack if one of their element is attacked (and if yes, then they will all attack at once). This can be achieved if the engaged troops are overwhelmed (too many adversaries). In your situation, if Army A can handle the opponent, B stays in reserve. If the opponent is too numerous (twice as many elements as A), then B has big changes to be committed. Unless all the frontage is saturated in this case the opponent despite being more numerous don't trigger the 'overwhelming' factor.
Frontage is cumulative for a given battle. Splitting troops in several stacks won't give you more frontage. The highest ranked officer of any stack, even if not involved, will lead the battle.
Hofstadter's Law: "It always takes longer than you expect, even when you take into account Hofstadter's law."