It's only sold by
Halfords, which makes it an "avoid" for me straight from the start - possibly unless you know your local store is good at bikes. I'd also prefer internal hub gears on that sort of bike, so you'd need to do less maintenance (the chain can be put away in a case and isn't dangling around near all the muck that gets splashed up). I'm a bit biased because I've got bikes with 1x6 and 3x7 derailleur gears and a 3-speed hub gear bike and I enjoy the hub gear bike most (when all else is equal which it rarely is).
I wouldn't worry too much about the number of gears - I feel that's less important than the range of the gears. 21 and 24 speed bikes (3x7 and 3x8) typically have a gear range of 300% or more, which will cope with most things. But a 7 or 8 speed hub gear will still give about 250% range - it's just that the steps between gears will be larger. If you're not racing-ish, that's probably not going to matter too much IMO.
I think a sit-up/town/roadster bike should be great for riding to school with children and around on cycle paths - they're no slouches if you want to ride on roads, either. The obvious choice would be a Pashley Princess, but they're expensive, beyond your budget at £600+ and Pashley are often criticised for high prices. Lower-priced possibilities look like the
Decathlon Elops 740
http://www.decathlon.co.uk/elops-740-dutch-style-city-bike-id_8303290.html or the Gazelle Classic which is on
http://www.cycle-heaven.co.uk/bikes/brands/gazelle/gazelle-classic-3-speed-women-s-2015/ and the very graphical
http://www.eastcoastbicycles.co.uk/Cycles.html somewhere. Both include some other possibilities including Dawes and Bobbin... I'm not sure about the Gazelle Classic for towing, actually. Towing probably wants a lower gear than most 3 speeds will have and then you'd need to lower the gearing - or more likely, get the shop to. Maybe a 5, 7 or 8 speed is a better bet.
Anyway, good luck and I hope you find something to ride that you love!