How can I prevent my kids to turn off the nextdns profile in the vpn&dns settings on the iphone?

I'm having the same problem.

To deactivate the user ability to deactivate/delete profiles configuration on Apple devices you need a MDM server/software/licence (depending on how many devices you want to supervise). The device will pass into a “supervised” mode. That mode are made for schools and entreprises, but that’s the only “official “ way.
 

I can suggest many software able to doing it.

While creating the configuration profiles you need to take careful action about:

1: setting the profile modifications by the user as “never”

2: setting the vpn modifications by the user as “never”

otherwise, even with NextDNS anti-bypass, if they successfully installed a vpn profil they may be able to bypass all the configuration.