Keep your password on the home print server in sync with your domain password so you won't be bothered with credentials....
(Or upgrade to XP to take advantage of the Credentials Manager.) Getting access to the Internet from home via the ICS gateway is just a matter of acquiring an address and configuration information from the ICS machine. Your domain affiliation would have no affect on that transaction. I doubt if you want to browse resources in the home network, so keeping the laptop in the work domain won't be a problem for locating resources.
Let me know if there is a particular problem you're having at home with the laptop because of its domain membership.
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