So the reinforcements were stuck behind an impassable cliff/mountain? If not then you probably should have moved your troops away from the edge of the map so the scots could march onto the battlefield.

I think the programmers should have made: A region around the edges, which causes your army to lose moral as they believe you are retreating (but not flee if not attacked); objectives which defenders must hold, such as a border fort, oasis or a large valley pass.