VPN access to Active Directory Domain

I have a central data center connecting to a series of remote offices (some of which are simply home offices) via VPN Tunnels. My question is should all of these client machines be able to access Active Directory and participate in the domain? Most of the sites are too small to run a server or domain controller. All can see the central DNS server and participate in the network without being a part of the domain. Each site has a separate subnet.

When I made one Windows 2000 Pro machine a domain member it returned a message (after a very long — 45 minute — login) that it could not find a domain controller for the domain.

Any thoughts are appreciated.