Ok, so all the Weasleys go to Hogwarts, as does Sirius and his brother. But let's say Luna had a sister. Does she have to go to Hogwarts, or could she go to another wizarding school? Does it have to do with where they live, like public school district lines?
They likely aren’t required to go to the school their siblings did.
There doesn’t seem to be anything that requires all the children in a wizarding family to attend the same school. It’s typical that they do, because the closest school would presumably remain the same, and if the parents liked a particular school enough to send one child there, then they’d probably send any other children they have there too, unless something drastically changes. However, this doesn’t seem to be because of any specific rule, it’s just what usually happens in the families we know of. In Britain, it’s not compulsory to send children to Hogwarts, rather than homeschool them or send them to a foreign school (except during the Dark Lord’s reign).
“Attendance is now compulsory for every young witch and wizard,’ he replied. ‘That was announced yesterday. It’s a change, because it was never obligatory before. Of course, nearly every witch and wizard in Britain has been educated at Hogwarts, but their parents had the right to teach them at home or send them abroad if they preferred.”
- Harry Potter and the Deathly Hallows, Chapter 11 (The Bribe)
There’s no reason why this shouldn’t apply to the individual children in a family, as well. For example, if one child particularly loved the Dark Arts, there doesn’t seem to be anything stopping their parents from sending them to Durmstrang, but still sending their other children to Hogwarts. It seems to be that wizarding parents, if they choose to send their child to school rather than homeschooling them, typically send their children to the closest school to where they live. From what Lupin says, it’s odd for British wizarding parents to choose an option other than Hogwarts.
The vast majority, then, send their children to Hogwarts. If they don’t want to do that for some reason (especially since it’s likely they have a compelling reason why they don’t want their child taught there and choose to go against the social norms of the British wizarding community), they wouldn’t want to send any of their children to that school. It’s unlikely to be a reason that’s specific to an individual child. If they dislike the Mudblood-loving headmaster and his teachings on Muggles to the point where they refuse to send their child to his school, unless he retires or something else changes, they wouldn’t want any of their children going there so wouldn’t send any others either.