I know this is a week or so old now but I wanted to answer it since I haven't seen anyone answer with this but I believe the Mjoll Grimsever quest not showing up greatly has to do with not being past the Horn of Jurgen Windcaller part of the Main Quest. I have no idea what it's prominence is to Mjoll herself but in making six characters, one with the intent to marry Mjoll, I noticed that in every single one that didn't have the option, what they had in common was not getting that far in the MQ, whereas the complete opposite happened for the others who had been, getting the option. To test it, I started a new character, console levelled them to 50, talked to Mjoll, she wouldn't give the Grimsever quest. Immediately did the MQ, finishing the Horn quest. I came back to her, bam, she gave me the quest to talk about her sword.
On turning in the quest make sure to complete it all the way, I think it was following learning a new Word of Power. Make sure that the UI shows "completed" on the Horn quest before talking to her again.
I'd be happy if anyone wanted to verify, although I'm pretty convinced.
Verified as NOT the answer, at least in my scenario. I am just about to call Mjoll a 'broken quest'; for me at least it has been a huge waste of time. Where is the CS when you need it?
Steps I have taken:
Started main quest, up to 'A Blade in the Dark'.
Became Thane of Riften.
Advanced level to 25.
Added Mjoll to marriage faction, follower faction.
Set Mjoll's relationshiprank to everything from 1 to 4, and wore / not worn Amulet of Mara in each rank.
Tried to start freeformriften09, (startquest) tried to finish same, (setstage 250).
One time I got Mjoll as a follower, all I did was set her relationshiprank to 3, and I got the folower dialogue. No sword, nothing. Just waltzed up, set the relationship, and off we went...