Grasping at straws here since I don't know the exact nature of your problem... How about some of that electronic freeze spray for the inside part and then heat the outside part with a torch or a heat gun real quick?

Stick the whole thing in the freezer overnight and then apply heat to the outside part real quick like and then give it a sharp rap to see if it will knock loose?

Maybe a hydraulic press pushing on a mandrel or pilot of the exact size on the inside part?