This is possible (for kiddo’s over 13, as Apple won’t grant Wallet use to under 13’s) - Create a Virtual Card in-app, then manually add the VC details to the Kiddo’s iPhone Apple Wallet and it adds the Virtual Card. No 
app needed on Kiddo’s phone - Kiddo taps phone at POS terminal with VC as the selected card and it deducts the amount from the Virtual Card balance just the same as any other card. It works really well as I get spending notifications. The only downside is they don’t have a physical card so can’t get emergency cash from non-tap ATM’s (the majority of ATM’s unfortunately)
I retain full control and they can use it with my permission. If they try & spend too much then they’ll get the nasty ‘declined’ experience. If they lose/misplace their phone, it still has the same security levels as anyone with a Monzo account and Google/Apple Pay anyway with Face ID security.