If it's a decent make like Samsonite I'd enquire about spare parts; as far as glues go I'd try a solvent type like polyweld, although there are polymers that solvents just won't touch.
Buy a new suitcase. Do you really want to be stuck on holiday with all your clothes locked in the bag or worse all your clothes over the baggage belt because the button snapped of in the hold of the plane
Bit of mild steel or aluminium (aloooominum if you can't manage the correct pronunciation). Angle grind and file to shape, couple of drilled holes and it's the strongest part of the entire case.