IAMAP, but I'd have thought that the galaxy would flatten everything out to a certain degree, but as you move to smaller scales, local gravity conditions would take over, for example: the planets being more tightly bound to the sun than they are to the Milky Way as a whole.
Q for a physic-y person - The earth orbits around the sun's equator, but its own equator is at an angle to the sun-planet plane (hence, seasons). Does the moon, then orbit around earth's equator (at an angle to the sun), or in the same plane as the sun's equator (or some other plane entirely)?