per wiki:
When you marry Mjoll, you can take everything in Aerin's house in Riften except for his bed. Therefore marrying Mjoll is one way to get a free house.
If you marry Mjoll and decide to move out of Riften, Aerin will move into your home as well. If you happen to kill Aerin, Mjoll will no longer be a follower.
This is not the case if Mjoll is following you at the time of your move. To prevent Aerin from ever moving in, tell Mjoll you're moving when she is actively your companion. If you need her to be replaced by someone else, tell her to wait. She will get bored and return to the new home, Aerin will remain in Riften, and you can recruit a new companion.
Mjoll will continue to be your follower if Aerin attacks you and dies as a result (ex: you are a blood-starved vampire or he is goaded into assault). This is another way to get him out of your house.
Mjoll will also continue to be your follower if your murder of Aerin is completely unobserved. This is easily accomplished by recruiting Mjoll as a follower and having her wait; after, simply wait until Aerin is alone in his house and kill him while hidden.
Mjoll can be recruited as a member of the Blades. If she is recruited, Aerin, if alive, will again follow her to Sky Haven temple.
Mjoll as a spouse, like other spouses, is considered essential, meaning she can't be killed by enemies, however, if in recovery mode she can be killed by the player as a number of other spouses can.