Question : Why did traffic route to localhost (127.0.1.1) instead of VPN (172.16.2.10)

Please help me understand more about tcp/ip routing.

About 6 weeks ago our home office staff started experiencing intermittant failure when required to authenticate their credentials on our corporate WAN (Microsoft Active Directory). Our Active Directory & DNS are outsourced by our corporate. I have no access to them. I finally fixed this problem by adding our corporate Domain Controllers to the hosts file. I am really glad this is Is fixed but I don't really understand why the entries in the hosts files fixed it.

Answer : Why did traffic route to localhost (127.0.1.1) instead of VPN (172.16.2.10)

nslookup is a good enough utility for that purpose, so if it worked before updating the hosts file, it means that DNS was working.
Other option is that your active directory service was directing your computer to use a different unresponsive DC to you instead of the one you use. You could try to browse your AD, if you have enough permissions. Try to use the RSAT tools.