Question:
Does the collision of Galaxies, in some way, go against the idea of a Big Bang?
Answer:
Not at all! The Big Bang thrust the Universe into an expansion that doesn't stop, that's true. But this is an expansion of space-time. Galaxies "collide" the same way that asteroids collide with planets, without expansion being brought up: for each case, the Universe is "motionless", because on a small scale you don't notice the expansion. And gravity, even among two galaxies, is much stronger that the effect of the Universe's expansion.