When you installed and activated with the same LiveID on your work PCs, you were not asked for the product key from the new box as you already had a subscription.
Each LiveID can only have one subscription and each subscription is valid for up to 3 PCs.
However, you won't be stopped (at this time) from activating more than 3 PCs with the same LiveID.
To resolve your current situation, create a new LiveID. Then uninstall OneCare and reinstall it from http://onecare.live.com.
Activate the first install with the new LiveID and use your second product key. Once activated, repeat on the other work PCs.
On a hub on the home PC, after you've reinstalled the work PCs, expand each work PC entry and select to remove that PC from your subscription.
-steve