I have two dogs-a male springer spaniel, and a female australian shepherd. What would they do, if something happened to me? Would these two stick together? Or would they battle it out for dominance? Suppose they were out in the woods, and I croaked-would they stay together? 
If the dogs have been together for any length of time, they’ve already figured out which one is dominant. You may be the alpha, but there would still be a hierarchy, at least until the submissive one figured out the dominant one couldn’t defend its territory.