I went to the woodworking table as a level 10 in handiness skill and there is no option for the wooden throne. So I made the toilet hoping that would complete the mission, I know it’s not the same but I tried it. Of course it didn’t work.
Also, I went to the cave and in my game it’s already broken into, so I explored it and it didn’t check off the mission from the list.
Did you claim the reward object Throne, by chance? This was a stopper for me on Week 2. I failed to claim an item, because I didn't really want it. Turns out, that's really not an option. So, I went back and claimed it then for good measure, I clicked Claim All. Did the trick for me.
