It sounds like you are describing a VPN (virtual private network). A VPN directs all traffic (whether http or other tcp/ip protocols) through a specific server, usually with the intent to encrypt traffic between the device and the VPN server.
However, encryption isn't necessary, and a VPN would have full control over routing, which means you could customize a VPN server to block specific requests. Or you could redirect requests to unsafe/undesirable websites to a 'block' page of your choosing.
Almost all android devices have VPN capabilities built-in. You should look into that technology. In order to force the user to go through the VPN, you will need an app that can be set as a device admin (a built-in, almost-root privilege that prevents the app from being removed) that would also set the VPN to be always on.
See this Android.SE question and answer for more details.