Thanks for the saves! Yeah, there was some weird behavior with that quest and I made a fix. Please download two files here and put them into your game's data folder along with other data files. Confirm the overwrite, then load your save and check your home cave again. The fix works even if you are in the cave from the start, so you don't need to prepare any other saves or start the game from the start.
Please ping me back if this solution fully solves the problem and I will roll it out to the public update.