Can you join a computer to two domains?
Solution 1:
Short answer: no.
Since you're talking about work and home domains, I don't imagine you can set up a trust between them. OTOH, if you're even allowed to join a personal PC to the domain at work, maybe it's a small, informal company?
Workarounds: Join the home domain and just map individual resources and give your work credential, or maybe set up a VM on the laptop that's joined to the work domain.
Edit: while looking into this a bit more (because it's something a few of our remote users have asked about), I came across Globesoft MultiNetwork Manager, which says it can join one computer to two domains and switch easily between them.
Solution 2:
Easiest way to handle this is to have your machine's "workgroup" be the same as the work domain... then have a UID on the local "workgroups" other machines the same as the uid for your work uid... then keep the passwords in sync... windows tries to 1st connect via the current uid/pwd (w/o the domain prefix), then if it doesn't authenticate, it prompts you... been years and years since I studied that, but been using it all along since winnt4
Solution 3:
You can partition your hard drive and have the machine dual boot into separate OS's. One for home one for work. That is about the only way.