My family has been testing this and have found that most of the newly added controls can be easily bypassed by simply going offline. The library control features, which seem to be ported from the old family view, seemingly work but everything else is easy enough to get around:

1. Time limits and scheduled time restrictions become immediately ineffective if offline or, from what I've seen, if the time/date on the computer are changed. This obviously means it works for online-only games and multiplayer components of others but for single-player, offline games, both the schedule and the time limits are effectively meaningless. (And related, requests for more time when the cause is the schedule rather than running out of a limit also don't seem to work - the request can be approved but the schedule takes priority regardless.)
   
2. Many screens which come up as blocked by default (e.g. the News tab of the store) load anyway if you click cancel.
   
3. Store restrictions can also be bypassed by going offline, quitting Steam, and then navigating to the blocked page. Of less concern since most kids won't have a credit card on the account is that you can add a blocked game to your cart while offline, then go online, proceed to checkout, click cancel on the blocked message, and then proceed to checkout anyway.

I feel like I'm forgetting something but for now, I think that's the gist of the problems we've seen.