Stop kid turning off data?

Depends on how they are doing it.

If they are going into the settings and deliberately turning it off then you'll need to stop them accessing the Settings. There are apps in the Play Store that can set a PIN or password before you can access other apps (of your choice), though I've never used one.

If they are pulling down the notification slide and hitting the quick settings toggle then you could (on most devices) edit the quick settings and remove that toggle from there.

Or there's the sociological fix: tell them that if they don't leave that setting alone you won't let them play with the phone .

 

Devices vary greatly, but on some of mine, inside the Developers Options, there is an option to force he device to always maintain a data connection even if Wi-Fi is available.

Generally, a device will automatically stop most cellular data flow whenever it can connect to a Wi-Fi source.
This is to conserve data, as data is usually the expensive and limited portion of a cellular plan.

Perhaps this setting can be used by you for your purposes.

If you have not opened Developers Options on the device, you must first unlock them.
The method to do this varies by device {of course, right?} but is usually quite easy.

The general gist of it, at least from the device that I am presently using for this answer, is:

Settings
System
About phone
Build number
{tap build number 7 times}

A small toast message will appear to let you know that 'You Are Now A Developer!'

Now back out to the homescreen, and:

Settings
System
Deveeloper options

Turn the switch on, and scroll through to find
Mobile data always active



Hopefully this, along with the suggestions from @Hadron , will achieve the desired results.

 

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