It was "her father's here unexpectedly" plus "Takako is acting oddly standoffish". So nothing as simple as meeting her dad, although it does leave the question of whether they have met at some point, or for that matter whether Shinobu has met Takako's brother.
But the fact that she worried about her clothes really screams "first impression". Do remember that this is the Shinobu that does not care at all what she wears, the fact that It's now important really points out to "ok time to show myself in the best possible light".
It's weird because, I'm pretty sure that Takako has been out to her family ( I do remember some scene with the brother ) and they don't seem to mind. Maybe they live quite a distance away? Still it's weird they haven't interacted over the years.
For that matter, have we had any insight into Shinobu's family at all?
I don't remember anything about her family at all now that you mention it.
Well, "parents of your significant other" is an important position in Japan. You need to meet them before marriage, make a good impression when dating, that sort of thing. So to show up dressed at your worst really isn't a good idea.
But in context, it's possible Shinobu is expecting something serious happened since she's acting weird when her dad's visiting. So even more, it would be bad showing up looking like a vagrant and she doesn't know how to address him, not knowing the situation.
