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The player can marry Mjoll if they possess and are wearing the Amulet of Mara. The player must also have completed her personal quest. She can be both a follower and a spouse simultaneously. When married, Mjoll opens a shop, and gives the player a profit of 100 Septims each day; everyday that you don't collect from her, it adds up.
Even when wedded with the player however, Aerin may sometimes continue following her. One solution to this particular bug is to kill Aerin. Alternatively, one may change followers for a time and then recruit Mjoll again, which can also resolve the issue. Methods killing Aerin without upsetting Mjoll are as follows:
The easiest way of killing Aerin when Mjoll is a companion, is telling Mjoll to wait inside a hold that is not Riften. Aerin will leave the hold and head back to Riften. He can be killed on the way back with no witnesses, and also without Mjoll hating you.
On PC, instead of directly killing him, you can use the console command "disable" while selecting him to make him disappear.
another way is to kill Aerin when Mjoll is a companion and is following you, followers are oblivious to crimes. (confirmed PS3)