Not Sure How to Describe This

Look at the sentence in the last panel, courtesy of Rabbits Against Magic.  Doesn’t feel quite right, does it?

That first preposition isn’t right somehow. Maybe I see a suggested contradiction between “in the opposite direction” and “to the White House.”

“Opposite” can stand by itself just fine:

They’re moving opposite the direction to the White House.

Or maybe something even simpler:

They’re moving away from the White House.

How would you smooth out that sentence?