Welcome to the forum!
One thing you *could* do is start your trip in Jersey or Inverness. This would save around £460 or so in taxes/fees between you as they are exempt from APD. The connection from there (in business) would be included for the same amount of avios.
However you would need to make your own way to JER/INV at the start and to make it worth it would probably want to stay for a night or two there. That would wipe out much of the saving, so you could instead view it as ‘we can get a wee trip to Jersey/Inverness for free’ rather than saving much cash.
Whether that extra travelling is tempting or not with a 10yo in tow is another matter but I’ll leave that with you.