if you're goign to push on a malleable pin, to try to drive it out, you need to remember that you'll be compressing and expanding the pin at the point of impact, binding it tighter.
given the crap metal probably involved, i'd reccomend taking a nice sharp nail, giving yourself a solid center mark in the pin/rivet and then well aimed application of a drill bit into the pin. use a drill bit ~7/8 the dia of the pin, or 5/4 the size of the pinway if you want to reassemble it tidily with a new (and bigger) pin (say like a machine screw so you don't have ot drill ti out again)