My understanding from Pipling's earlier posts is that
a) they are residents of the property in question
b) their time is currently split between Liphook Crescent (their home), and the living quarters at the new nursery branch while they set it up - not as a permanent move
c) they would be spending more time at their family home if the atmosphere in the street towards them personally, and their young children, was not currently so frosty - and who can blame them for wanting to keep their kids out of something that is not their (the kids, I mean) fault/problem!

This means that it is "someone running a ... business from where they still live"

(Please note: I have omitted the word "small" from the quote, as I am making no judgement about the size of it, but it's hardly a chain the size of the Townsend Montessori one, or Pitta Patta, which has permission for 48 children at once, rather than the 24 at Piplings, and is also on a quiet residential street)