I'm having a hard time piecing your situation together based on what you've written. DHCP at remote site is handled by an ASA 5510, site-to-site VPN was there and still may be there, you have 2 DCs but I'm still unclear about which one you think is down.
My guess is that if one of your DCs went down, if the site-to-site VPN is still working correctly, if you can log into the computers, and if you successfully resolve DNS after running ipconfig /flushdns, then my guess is that you're probably going to be fine. Domain Member PCs can be logged into when offsite as the credentials are stored locally once a user has logged into the computer. As long as you have the other services/resources available via a site-to-site vpn, then it should be okay in your situation. That said, if the remote site can reach the DC at the main site, you may see...
