Can't remote desktop via VPN from outside the domain

I'm having a problem trying to remote desktop, with very specific circumstances. With all my HP Probook 430's and 450's, running Windows 7 Professional 64-bit. When they're outside of the domain at a remote site, connected successfully via VPN, they're supposed to be able to remote desktop to various computers inside our domain at our main site. But they can't. Instead I get the general error (attached). But none of the problems in the error are true.

Here are the odd circumstances. I have other machines - HP desktops, other laptops, etc. that can remote in via the same connection from the same remote site. So I know the connection is fine and I know our server-side VPN/firewall is fine. But also, these same HP laptops can remote connect to the target systems just fine when they're inside the domain at the home site. So their remote desktop connection software on the laptops is working fine. But something changes when those laptops go offsite that prevents them from connecting, and I can't tell what it is.

I've tried enabling and disabling the firewall on the laptops, but nothing's changed. I've tried disabling Symantec Endpoint Protection as well. I've also tried using the local admin login instead of the domain AD account login. Nothing's affected the issue.

Any ideas where to go from here?
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