Above questions all relevent.
This is an awkward one really, as does the dealer disagree with Toyota tyre pressure in the handbook/sticker inside the door shut, on the tyres it left the factory with ?
Presumably you have been checking pressures cold given in the handbook/sticker, which is what Toyota themselves recommend for loaded or unloaded situations. That figure would have come from the tyre manufacturer anyway, and is on the sidewall of the tyres as maximum. Check that.
A bit of a grey area really, as pressures stated by vehicle manufacturers are not usually tyre specific, just a blanket figure/starting point, but you can only start there.
A lot of us do tweak tyre pressures to suit our cruisers/conditions, and some tyres do wear faster than others, due to different rubber compounds used.
Is it all of the tyres, or just front or rear - have they all been rotated to share any uneven wear, and is the wear on specific areas ?
Given it has only done school runs, the driving style should be moderate and not aggressive.
Unfortunately, dealers/manufacturers dont like admitting they are wrong, and in any case, you can't prove that you have diligently kept to the recommended pressures.
Sorry, can't be more specific, maybe answers to questions may throw up something regarding the wear aspect with other members.