general relativity - How do you explain the observed fact that "black hole" objects move?

As per Newton objects with mass attract each other, and per Einstein this is further explained by saying that mass warps space-time. So a massive object makes a "dent" into space-time, a gravity well. I have taken to visualizing this as placing a object on a rubber sheet and the resulting dent, being the gravity field. So obviously placing two objects on the sheet not to far from each other will make the dents overlap, and the object will roll towards each other. BUT for a BLACKHOLE, this is not a dent. It's a cut or rupture in the rubber sheet. Furthermore, space-time is constantly falling INTO the blackhole, and everything else that exists in space-time, including light. So a blackhole is not just a super-massive object, it's really a hole, and how can a hole move? How does it react to the gravity pull of a nearby object, when everything just falls thru it? Thanks!