Sounds like a mid-size people carrier would fit the bill, as the kiddies are still small. Something like a VW Touran/Ford Focus C-Max/Vauxhall Zafira? Not the most interesting drive, any of them, but generally inoffensive and perfect for a growing family. Most will be diesel (as the government encouraged people to buy them before the U-turn), but there will be petrols out there - although they're likely to attract a premium these days.
Cheers,
Plug