iOS is tough, I jailbroke my kid's iPad and found an app that keeps track of what apps are running for how long, which was a decent balance between the restricted level of guided access and wide open. Trust but verify. But it would be nice if Apple had some better features or allowed apps to do more.
I used that in combination with OpenDNS which lets you control what sites they can see and such. A bit more flexible than the router route as it doesn't depend on going through the home network.
I've also been playing a bit with this:
https://www.qustodio.com/en/?x
Only been using it on the PC but it seems to work pretty well, alerts when they go to a restricted site which is nice, can set different levels for different kids, set time limits, and gives a nice view of what they've been doing.