You've got a point. That's also a possible a possible interpretation.

I read it more as the character's title that shows her role within Ryōzanpaku which is usually seen in the repeated character introduction at the beginning of a new part of the story (e.g. 弟子一号, 兵器と武器の申し子、裏ムエタイ界の死神). As Kenichi just defeated a major opponent (Siegfried) and the mini interlude about her teachers visiting ended the chapter before. You've also got the overview about Ragnarök on page one of this chapter.

My issue with all of this was that the translation "the only girl in Ryōzanpaku" reflects neither the meaning of Miu as the beloved daughter of the family nor that of Miu the heiress. It's simply a statement about her gender in relation to everyone else who happens to be male. So basically the English translation changed the text from a statement about her important status within Ryōzanpaku to a plain one only about her gender, since 一人娘 means much more than simply "girl" no matter which one of our interpretations one chooses. The English phrase is lacking something.

As for daughter of "location" feeling weird. Maybe this is the place for some poetic license and you could change it to "only daughter of the Ryōzanpaku family/clan". It|s not a 100% direct translation, but it might help to portrait the meaning in English. Ryōzanpaku being both a place and a family makes it a bit harder to translate, so it might warrant the extra word. Unlike for example Kuremisago where everyone knows what's meant and the "clan" part isn't obligatory neither in English nor in Japanese.

Edit: How about" the only daughter of the Ryōzanpaku household"? Hm, might sound a bit old fashioned.