Red shift occurs when a source of light is moving away from a viewer's perspective, and blue shift occurs when it is moving towards a viewer's perspective. According to the Big Bang theory everything is moving outward and away from everything else, yet the blue shift occurs as the Andromeda galaxy comes closer to us every day. How can this be?
If gravity is pulling them together, then it should have stopped them from moving apart from each other to begin with. Fairly simple.
Not every force in the universe is equal.
Why do you think a space shuttle can escape the Earth's gravitational field? Because it exerts a greater amount of force. An 'explosion' exerts a great deal of force initially, but after the reaction, there is no further energy being expended. If the reaction has propelled the Milky Way & Andromeda galaxies outward but close together - which could easily happen; after all, shrapnel from a TNT explosive often flies in the same direction side by side. The immense gravity of two galaxies 'nearby' is pulling them closer.
You call this stuff 'fairly simple' but it's actually incredibly complex cosmology.