Account with parental controls enabled breaks proxy use
I've found a solution for this problem. Running proxy software on the Mac will override Apple's built-in proxy used for parental controls. In this case I used squid via the SquidMan package as follows:


Install the SquidMan package to the administrator account. Ensure SquidMan is configured to run at startup.
In SquidMan's preferences enable use of a parental control proxy, and point it to your router that is running squid (at 192.x.x.x, port 3128).
In the controlled account configure the browser to use a proxy and point it to the one created by SquidMan (at localhost, port 8080)


In this way Internet access from the controlled account will be routed through SquidMan to the specified proxy coming from the router.

One caveat of bypassing the Apple proxy is that the Parental Controls will no longer keep a history of visited websites. However you can configure Squid on your router to keep access logs that provide much more information than Apple's parental controls are capable of.