I'm not sure of the benefit of delaying logging into Parental Controls until Mail.app starts, though I assume there's good reason for this.

What might be most useful is if you could describe exactly how you log into Parental Controls as opposed to simply logging into the mail server (I'd think the mail login would be in each user's keychain). How do you invoke the PC login? Can you do this login from within Terminal? (If so, it can probably be scripted.)

I'm imagining your router is basically acting as a mail proxy, but this may not be a good model. If you can give us some details about the steps required to perform both PC and mail server logins, as well as about how your users mail accounts are set up relative to the computer's user accounts, some one here might be able to piece together a solution.

In answer to your question, I don't know of any Mail.app startup handle you could use for this (I use GyazMail btw, so my familarity with Mail is a bit minimal), but you could easily set up a script to periodically check whether Mail.app is running and trigger the required login script.

I agree - it would seem to me that this would be better done as a login item - so it happens automatically at login.

Anyway, one way of running an AppleScript when an app starts up is to replace the app with a wrapper AppleScript that does whatever you want and then launches the (renamed) app.