All the "local" galaxies,called the Local Group are well researched and their positions and velocities relative to The Milky Way are well known.
You rightly point out that if we look at, say, the far side of the Milky Way we are looking at light from stars emitted perhaps 50,000 years ago and much more time for further away places, I think the Andromeda galaxy (the other Biggie in the Local Group, along with us) is 2,000,000 light years out.
The point is that there has not been enough time for the other galaxies to impact on the Milky way yet, although those collisions will happen eventually, (Andromeda is hurtling towards us at about 600 kilometers per second)
Hope this helps, if not , reply and I'll try to explain more.