The fact that you say "Normanish places" makes me think you might secretly be thinking of the Angevin Empire. But the fact that you are asking about "teaching schedules" and "the qualifications of tutors" makes me think that you might not actually know anything about what you are looking for. What gender and age(s) are the kids in question? And, importantly, what subjects are involved? Your likeliest bet, really, is Some Guy who knows Latin and has both minor orders and lovely manners. You don't get celebrity tutors (except Abelard, which becomes, famously, a whole situation.)