Remote management requires a separate parental device.
Screen Sharing and Parental Controls, implemented directly on the device.
Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support
Another potential option is to shut down Wi-Fi access on a schedule. That might be an old-school mechanical timer on the Wi-Fi router power connection, or router-based controls.
That written… Kids are good at bypassing all of these features (whether iPhone or Android or router or otherwise), and learning more about their parents than their parents might intend, or might even realize, in the process of bypassing. Kids will stay contained only if they are willing to be contained. Anything you can do can here be bypassed on an allowance-scale budget too, if the youngster is inclined. Kids are good at shoulder surfing or guessing passwords, and at communicating with other kids about security, and at finding creative bypasses for established blocks.
Pragmatically, I’ve found these parental control features are only really useful for keeping parents from causing issues with their own devices that the kids would otherwise then have to fix.