Ok, so I ordered a replacement handle. All looks right with it, but what I can't figure out is this post alongside the locking mechanism. The old lock cover part seem to have had something rip out from the inside of it. That post doesn't seem to want to come off (unscrew), but the new part has a threaded brass fitting that seems like it would screw on where the old one has come off. (see pics)

Does anyone have experience with this? I don't want to apply too much pressure and find myself in a hole!

 

I have never changed/replaced one on a Hyundai, but just about all the time, you need to get to everything from inside the door.. That requires the interior covering be removed so access to the lock assy is permitted.
If it were all that easy , just about anyone could get into your vehicle and they try to make it pretty difficult to do.