Between 67 and 69 Chrysler made a key blank, pin size & pin spacing change to their pin tumbler that fits into the switch.
I suspect that your tumbler is worn, has weak springs, gummed up from too much lubricant over the years, and key is cut too deep from factory dimension causing it to hang-up. It is a simple fix for a lock smith to repair. I would also bring your drivers door lock to him as that lock is most likely is in need of new pins & springs as well.