This is adorable!

(Though I'm not entirely clear, canon-wise, on when or if Syuko reconciled with her parents -- if I'm remembering right, they kicked her out of the house after an argument, which led to her living on the street when she was scouted. I've always kind of headcanoned that into being over Syuko's LGBTQ+ status, but that might be just my perspective on the sorts of things that parents make their children homeless over.)

In CGSS, you scout Syuko while she's minding the family store, then she gets kicked out for refusing to work some time later and shows up to an audition. Even then, she doesn't seem to be on poor terms with her parents, as she talks to them over the phone after she passes the audition and they seem supportive of her new career. She also has several lines in both CGSS and Mobage CG where she mentions either staying with her parents in Kyoto or getting confections from the family store. You can also see the first time she actually visits home again in the Bi Ni Iri event story.

Thanks for that! I've a lot sketchier knowledge of the direct canon than I think sometimes.