Rod 1 - you're not alone. I'm an FI often taking kids up in the back when Dad's doing his trial lesson and they're nearly always sick.
But, I'm all for kids in the back - I've seen quite a few dogs and cats in the backs of planes too and they all seem to love it. Just take a bag - I once had generously to donate my headset case to the cause!
On a serious note though, make sure your PFLs are up to scratch and you've worked out how you're gonna get the bairn out in an emergency evac. Allocate roles and order of evac, etc.