This is another one of those Mangas where I think the Author tries to Force the Protagonist into a situation when they don't need to do that. And that's bad because it ultimately just robs the MC of Agency. Granted this story has that going on far less than other similar stories, which honestly just highlights how unnecessary it all was.
Just let the Protagonist actually Choose this. It wouldn't even be hard with this Protagonist since he's already a guy who will tear his hands open to help a stranger. I think you could completely remove the Rat Character and just have chapter 2-3 be the two MCs interacting, with Dude deciding after watching her take care of the kids and learn more about who she is to help her. This could also give you a chance to explain the Dude's magic earlier, and perhaps work that into the story.
Basically, remove all of the ridiculous requirements and conditions and focus the story on the relationship between the protagonists.
This also gives you the opportunity for a great joke because with chapter 2-3 being the MCs just interacting with no one else getting involved, possibly up on the Fang Rock, before deciding in this chapter that she should see about living with him in a better location, you could have chapter 3 end with him bringing her home to his family, who are worried because he's been gone for an entire day or more, and he's just like "Oh yeah by the way this is Mai Waifu we have 2 Kids can she live with us here?"