Post here if you need help getting started with Daggerfall Unity or just want to clarify a potential bug. Questions about playing or modding classic Daggerfall should be posted to Community.
I think I somehow broke the quest. I retrieved the turquoise and returned to the quest giver, but he won't talk to me. I attached a save.
The only thing I can think of that could have caused the issue is that I hit the cousin, then saw the turquoise, took it, and ran away without killing him. So possibly the quest locked me into that line, even though I have the item which should let me finish.
I am on 0.16.0 and don't have any mods that I would think would mess with that the quest code.
I can't imagine what's going on, since the quest script is properly written and you have the gem. I fixed your save at least, so you'll at least be able to progress.