Why can I see the Andromeda Galaxy despite Milky Way's rotation? Okay ... so, I woke up from a dream last night wherein I was (apparently) attempting to devise a time-keeping system for interstellar travel (similar to the stardate system used in Star Trek). In the dream, I was attempting to correlate our current calendar, based on Earth's movements relative to the sun, with this fictitious calendar using the positions of intergalactic stellar bodies in comparison to Milky Way. (i.e., What if we could tell time based on the way other galaxies moved in relation to our own galaxy?)

So, in the dream, I was understanding that Milky Way is a spiral galaxy which rotates around a galactic center. That Earth is toward the middle-end of one arm of Milky Way's spirals. That almost every star we see in the night sky is inside Milky Way with us, and that the galaxy Andromeda is a great distance beyond Milky Way and can be seen in the night sky over Earth in the same location (between constellations Cassiopeia and Pegasus) every night since (at least) 10th century C.E.  

Assuming Milky Way was graphed on a flat sheet of paper with the Galactic Center plotted at X=0,Y=0, and the arm which contains Earth was located at X=0,Y=-δ, and also assuming the galaxy Andromeda can be seen in earth's sky from this position ... why then, when Milky Way rotates around it's galactic center so that the arm which contains Earth is located at X=+δ,Y=0 (a rotation of 90°), or even X=0,Y=+δ (a rotation of 180°) is the galaxy Andromeda still visible in the same location in the sky?

Unless the galaxy Andromeda is in some sort of galactic-synchronous orbit with Milky Way (which seems unlikely since most of the posts referencing Andromeda here deal with the collision of the two galaxies), then, in the in either of the second rotational positions listed above, Andromeda should no longer be visible.

What am I missing? Why does Andromeda, which is not a part of Milky Way, only move in the night sky in relation to Earth's seasons and not in relation to any other galactic movement?
As barrycarter already pointed out, it is due to the huge time it takes for the milky way to rotate.

For once, as he pointed out, the stars in an orbit similar like the sun take about 250 million years for one full revolution around the center of the galaxy. If you put that in a relation to an earth year and take our civilization of roughy 6000 years of keeping records in comparison, we exist roughy 12 minutes of our galactic year. If you only take the last 150 years of the modern era, it's down to 18 seconds.

So if you compare that, how much does Earth move around the sun in 18 seconds? That is about how much Andromeda has apparently moved relative to the constellations in the night sky since we can capture visual images on film.