I've seen a few other posts about creating parental controls using MDM Profiles to prevent other devices from opening certain apps:
Would it be possible to use this method to allows the user to prevent access to their own apps on their own device?
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In these systems, the devices are managed by an MDM server which pushes profiles to enrolled devices.
There is no "parent" or "child" concept in MDM itself, just devices which have profiles assigned. So you could place restrictions on any device, even if it was associated with a "parent", as the management comes from the MDM server, not the device.
However, a "parent" likely has the passwords needed to remove the profile from their device or change the profile associated with their device in the MDM console, so I am not sure how effective this would ultimately be.
If what you are asking is if you can externally lock certain apps on a device, then you would most likely need the apps of which you are locking to have some sort of support for the parental controls app. Something like external whitelisting of Apple ID's.
This is because as of iOS 10, the structure of the system doesn't allow one app tamper with another, unless permissions are given, which makes sense. Nobody wants their app to be tampered with by a random person.
To put it bluntly, in theory, this is possible, but only if the app that the person wants to lock gives permission. Other apps wouldn't work.