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There are some commercial products that act not just as inbound firewalls but also outbound firewalls that can be installed and restricted and require a password just as you want. If she has full admin access she'd be able to remove the software or perhaps delete its configuration files. She may not be that smart, and you could audit it automatically every day/week to see if she messed with it.
Your best bet is to take away admin access and give her "power user" access and tweak her permissions so that she can still install device drivers, install software, etc... but still can't do certain things like remove the firewall.
Unfortunately most of the really powerful auditing and control software suites are very expensive, geared at organizations with thousands of users in the field. They fit your solution well, but aren't practical for a single user. You'd be better off just firing the offending user and hiring someone you can trust.