I'm thinking that a fair number of mage children (who are permitted to) generally get sent to a human-run boarding school during their childhood - similar base curriculum to normal public schools, but with elective courses of study during what would normally be "high school", to give students some sort of trade skill. "Service Skills" classes most likely taught by either a turned vampire or a retired mage are mandatory, and train students to be able to successfully live alongside vampires.

Mage children born in the service of vampires who disagree with allowing mages to get their childhood education would be raised more like slaves or servants, whereas those permitted to go to human-owned lower education establishments are trained to behave more as equals - lifelong business partners or butlers, more or less.

Contact with family is usually limited during the stay at the boarding schools in order to help them get used to the sort of environment they'll be working in as adults - under someone else's constant eye, often with very strict rules and unreasonable requests.

Normal human schools might also be a possibility for mage children too young to use their talents, but I'm not sure what sort of rules would go into that sort of thing.

Think 1850-1920 boarding school culture. The treaty between humans and vampires has likely stifled certain aspects of social progress, and some schools are more prone to corporal punishment than others.