The solar system's rotation is about the center of the galaxy so that would be the natural pick for an inertial reference frame, or the supermassive black hole believed to be in the center.
The center of the galaxy isn't rotating, it's just a point, no? Picking the criteria for such a point would be difficult and tracking it even more so, but what's the alternative?
A black hole is a point. Its size is zero, regardless of its mass. Its event horizon has a size, but we don't need to care about that.
We do, however, need to care about the all the stuff that's revolving around that point, because even a slight imbalance will cause the galactic center of mass (barycenter) to move away from the black hole. Things get pretty wobbly out there.
Since it's well agreed that virtually every galaxy (spiral or elliptical) has a central supermassive black hole, it's fair at this point to call it part of the galaxy.
