@AnthonyWherry,

I know that there are cases where existing traffic, such as a discord voice chat, will continue through the parental controls as the function operates by blocking new incoming and outgoing requests, but this doesn't necessarily fit the bill.

I do have to say that what you are experiencing is not usual, especially since the pause function can still block the connections. It does seem that there are users that have reported similar behaviors with other network-level parental controls not working with chromebooks.

From a quick glance, a few users mentioned that it looks like there may be settings enabled for either the network or browser on the Chromebook that causes the device to use a DNS server that is different from what is set on the network. This does somewhat make sense, since the pause function of the network looks at the connected device as a whole, rather than the traffic.

Since the parental control service is run by google, and your daughter is completely in the Google ecosystem with a Chromebook, I would honestly recommend looking at the options offered for just their services. No matter what, these will be the most effective methods as the traffic will be blocked at Google's server, rather than by your router. 

  @AnthonyWherry,

Unfortunately, privacy has become such an important factor when buying devices that many controls have been added. While beneficial in most cases, it also makes parental controls a nightmare and a half due to how many workarounds there are. Our team has been hard at work to try and create new methods of detecting these workarounds when connected to your network, and you should begin to see some of these features soon. At CES, HomeShield 3.0 was announced, which includes a new KidShield program that will allow parents finite control over network activity and better control over what is and isn't allowed on your family's devices. We have not seen too too much on the release, however, we should see the features added soon.