Hi Natasha2992,
Thanks for the post in Apple Support Communities. I see you'd like to disable private browsing on your children's iOS devices.
You can do this using restrictions on the device, detailed here: Use parental controls on your child's iPhone, iPad, and iPod touch. For this type of restriction specifically, you'd tap Settings > Screen Time > Content & Privacy Restrictions > Content Restrictions > Web Content. It sounds like "Unrestricted access" is likely selected currently. Changing this to either of the other options would disable the Private Browsing function.
Cheers!