When hurricanes get close enough to each other they do spin around each other in the Fujiwara effect, as Lee-Delray said, however, they can begin interacting even before that. The outflow from the systems will disrupt each other, acting as shear. And if they get close enough(very, very close) the two circulations can disrupt the inflow to each other as well. Generally both storms weaken when they get too close.

In the case of Hanna vs Ike...Hanna has very establish outflow to the east an south, extending many hundreds of miles away from the center, Ike, while having a better overall structure, doesn't have near the outflow to the west of the center to combat Hanna's large envelope of outflow extending past the Leeward Islands. It would seem likely that Ike would come out worse in this scenario, but it wouldn't be good for either storm.