Apple - Password Protect AirPrint

You have multiple ways of blocking the kids from accessing the printers:

Depending on the make and model of the printer, you could setup authentication on the printer. This way users will have to enter the username and password for the printer the first time they AirPrint something. This has to be done on the printer.

Depending on the make and model of your network equipment, you can set up a seperate network for the kids's iPads that is not allowed to AirPrint (i.e. has no network access to the printers). Even though the teachers are also using iPads, this can work, as you would still have the ordinary WIFi where the teacher's iPad can connect to access the printers.

Finally, as you indicate you prefer a solution where the restriction is done from the iPad, you can change the setup of the kids' iPads so that they're not allowed to AirPrint at all.

This can be done from a MDM setup, if you have one already. You can then specifically select a number of iPads, and then restrict access to AirPrint.

If you haven't got MDM, you can install "Apple Configurator 2" (free download from the App Store) on a Mac, and connect each iPad to set them up as supervised and block access to AirPrint. Note that usually iPads will be wiped when adding them as supervised devices.

You can find the user guide for "Apple Configurator 2" here:

https://support.apple.com/en-gb/guide/apple-configurator-2/welcome/mac