You could have a look round princes risborough.
Be careful though. If HS2 work ever begins, it will make the journey from Risboro' to Aylesbury difficult. That side of Aylesbury will suffer severe road disruption during construction.
Ugh...forgot about that, will it not cause disruption everywhere round aylesbury way for a while?
Risborough is supposed to be getting new houses, it has for 15 years, when I lived there the farmers were all rubbing their hands in glee.( that had the favoured land. ) This was raised again last week, so I guess it is time-tabled still by those in the know, so maybe the op could investigate that a bit too if they like new developments.
Op Does your daughters friendly cousin, presumably your sibling or sibling in law's daughter live locally to the school, or are they based at a distance?