Cannot reinsert my caps lock key after removal

I think it's just a matter of getting all the parts aligned correctly. I'd start with trying to get the smaller piece in the second photo to click into place with the part that's still attached to the keycap. Once you've accomplished that, you should be able to get the key to snap back into its seat. For that last step, I suggest trying to get the metal bar to click onto the keycap first, then rotate the whole assembly down and with any luck, it'll successfully click into place.

Hope this helps!