Sounds more like the network the VPN connection puts you in has trouble making kerberos connections to domain controllers, but NTLM connections work fine (kerb might be blocked). The errors are likely bogus if you can get #1 to work - if the computer is connected to a domain it's going to want to use Kerb before NTLM, and if the machine still has (what it thinks is) a viable kerb ticket, it's going to try and validate that with a DC (to achieve auth), and if this fails, so does the connection.
This may not actually be the case, of course, but it sure has the symptoms of it.