The Tikz manual gives "edge from parent" construct.
But it is peculiar (it changes all the edges in subtree and some nodes).
How to color and thicken exactly one edge?
As Mikael mentioned in his answer to your previous question, I don't think this is actually a bug, but simply how TikZ works. So the solution to the problem is to change a specific branch, and then change it back on its daughters. As you ask in your comment, you can define two styles for plain and emphasized edges respectively, to save you some typing: