That quest works better when you are given it rather than stumbling upon it. Its one of the possible quest options given by the Jarls as I understand it. At least that how I got the quest.
Now the problem for me is that I had actually entered Mistwatch from the mountains and thus actually worked my way down rather than up. Now if I remember correctly, Fjola offered me the Ring, so I took it and kindly got the fella to leave. Broken hearted but then I know from personal experience that scum such as her are very welcome in the jungle, so be it if she won't listen to reason. This is not an uncommon story in real life, afterall. Anyway I digress. I then went up to report to her and the quest finished. Then for some reason I heard her draw so I turned around and showed her the true value of a husband

Horrible I know, but such is the moral quandry is it not?
So what i suggest you do is roll back to a save before you enter Mistwatch and do it again. I did actually try other ways all resulted in having to report to a dead Fjola which I obviously cannot do. Hope this helps.