The primary means to turn Muiri into a marriage candidate is to join the Dark Brotherhood and work your way through the questline until you’re given a quest to carry out a hit requested by Muiri. Basically, your wife to be is a cold-hearted contract killer, or at least, someone who hires contract killers. The other, more thorny issue, is the nature of that problem you solved, and how you need to solve it.
Although you can solve her dialogue issue with the Unofficial Skyrim Special Edition Patch mod. One is that she will constantly thank you for solving her problem. That being said, there are a few downsides to marrying Muiri. On top of that, she’s often heralded as being one of the most attractive female NPC’s. If you’re an alchemist and looking for a female spouse you may want to consider Muiri as a marriage candidate, as she is the only female marriageable dedicated alchemist in the game.
Why wouldn’t I be? Are you… interested in me?” Muiri’s mARRIAGE Dialogue
“Is that an Amulet of Mara? I’m surprised someone like you isn’t spoken for. Muiri Muiri in the Hag’s Cure in Markarth
