[Rachelsdad]

I would look at using a drift to drive out the pin shown at the top of your first picture (the pin which appears to have a head on it on the "inside" end). I don't think those are threaded, but just pressed in. Once that pin has been driven out, I think the assembly will "lift" off of the other one (lift is the wrong word, but fits based on the orientation of the latch in your first picture).

Be mindful of the spring. You might want to remove that first, if you can, to get it out of the way.

If anything else comes to mind or if I find anything, I'll follow up. Good luck.

Disclaimer: This is all just guessing on my part from looking at your pics, and desirable results are not guaranteed. I searched the net and believe it or not, could not find *one* hit - not even for a silly YouTube video - describing the latch disassembly or handle replacement. I searched for "61 62 63 64 full size gm," impala, pontiac, oldsmobile, buick, cadillac (they all used those very same latches in those years).