Get on board, little children;
Get on board, little children;
Get on board, little children.
Der's room for many a more!"


...just another way of saying, here comes my two cents:

1. Terribly wrong -- terribly is used as an intensifier that our ears immediately accept because we're accustomed to hearing people refer to situations, people, things, and so on, as being "terribly this" and "terribly that":

terribly good sense of humor

The same goes for awfully:

awfully good movie!

However, badly, an often used adverb, is not used as an intensifier to the degree that terribly and awfully are.


2. Yes! In a strictly grammatical sense -- or in an awfully strict grammatical sense, badly can function as an adverb modifying the adjective wrong.

Problem is: The concept of wrongness subsumes badness. We think of something wrong as being something that needs to be made right or as something that should have been done right. So, by saying something is badly wrong rings terribly redundantly to my sensibility.

To say something is terribly wrong doesn't sound redundant because terribly sounds like a common, traditional intensifier. But to say something is badly wrong sounds awkward because bad and wrong are closely associated in fundamental meanings.


3. After having written about badly wrong for five minutes now, my ear has become accustomed to badly wrong turn, and I will become terribly happy to use the phrase every chance I get from this point onward. And, if, instead, my language takes a badly wrong turn in doing so, I would be awfully happy if one of you would turn me around and set me back on the straight and narrow.


Taking an awfully, terribly, badly wrong turn,
WrongWind

"badly wrong turn" wouldn't have made it past The New Yorker editors, I don't believe.