On 1, I second old Thorns. Or you can join Champneys. Lastly is the Everyone at Alton. A bit of a trek, but some really cool climbing stuff, classes, soft play, and everything is new topped off with a nice spa. and works with a Taro platinum membership.
On 2, you sound a bit ridiculous. Guildford has a population about 10 times the size of Petersfield. Of course some of the facilities in what is effectively a city are going to be larger than a small town, but the Lido is clean, friendly and actually quite new, so a bit of perspective wouldn’t go amiss. There is no ‘shame’ there whatsoever.
On 3, more ‘shame’. There is a brand new cinema in Liphook which isn’t far to drive at all, and the Petersfield nightlife is largely pubs, bars and some nice restaurants, but that’s where a direct and regular train service to Guildford and Portsmouth and even Waterloo comes in. Great stuff nearby but not in your face, and we don’t have to deal with the mess, noise or fallout.
its not clear to me that you’ve grasped what is quite unique about Petersfield which is a town with a gorgeous Heath, Lido, playing fields and nice community, packed with some good national (Waitrose, Waterstones, Robert Dyas) type shops, as well as a bunch of independents (deli, Annie Jones, Six restaurant etc.) which is close to everything (whether via road or rail) but manages itself to go slightly under the radar and avoid the fallout, crime, anti-social behaviour of larger places, which is exactly what we were looking to avoid when we left London.
Feels like you might be more suited to somewhere a bit larger, although that will inevitably come with those issues, and as a parent to two young children, that simply wasn’t worth the trade-off for us, particularly when it’s all so easy to get to anyway.