|MadSci Network: Astronomy|
Part of the problem here is a confusion between rotation and revolution. Think of rotation as spinning, and revolution as orbiting.
The answer to question 902372110.As says that the spin of stars is not necessarily related to the Galactic rotation. The rotation of the Galaxy as a whole is of course defined by the orbits (revolution) of the stars, and the vast majority of stars we see orbit the Galaxy in the same direction. That's why it has a plane at all!
While the stars revolve around the center of the Galaxy, they spin on their own axis like a top. The direction of that axis has nothing necessarily to do with the Galaxy; they can point any which way.
The idea is, a star forms from a gas cloud. This cloud is orbiting the center of the Galaxy, so the stars that form from it will also orbit the Galaxy. However, that cloud may suffer a random collision and collapse. When it does, it itself starts to spin, and the direction of that spin depends far more on internal dynamics than the outside Galaxy. So while the stars that form from it will orbit the Galaxy, they will spin on their own axes randomly.
That is why the ecliptic, the plane of Earth's orbit, is not aligned with the plane of the Galaxy. As a matter of fact, they are currently tilted with respect to one another by about 60 degrees!
Try the links in the MadSci Library for more information on Astronomy.