Sophie's situation appears to be the opposite of Molly's. Her okaasan has to tell her, after three months, that they would like her to help out more in the family, and she is chagrinned to realize that she had been cocooned, even though she thought she was participating in the "inside" life of the family. Sophie's okaasan appears to be more outspoken than Peter's, and you may think her to be more "western" because of this. But it is more likely that okaasan would not have spoken to Sophie so directly had she not already begun to proceed beyond the entry point. Sophie is not like Peter, and Sophie is more like Molly than you might guess. Just as Molly's okaasan had to develop a relationship with trust in order to presume that Molly will cook for otoosan, Sophie's okaasan had to develop enough trust in Sophie to tell her directly what she is supposed to do (when this isn't ordinarily done). Even though Sophie hasn't intuited as well as Molly (or Erika) what her family needs, her okaasan's "help" enabled her to reach a more "inside" status, as you will see later. Sophie's difficulty was that, in contrast to Kaarina, her timing in helping the family was too slow.
Mark seems clueless about the actual dynamics of his homestay. (Does Mark remind you of anybody else here?) He mistakes what is really deference for being "comfortable without being too deep" and thinks that, although he is still a guest he is also becoming "friends" with his family. The real difficulty here is that if he doesn't really see or interact with his family a whole lot, there is no way for him to establish a relationship with them. Interaction is crucial, and is the basis on which Erika, Molly, and Sophie were all able to negotiate their way past the entry hurdle.