ODBC on the Internet is not very secure...also performs badly. A couple of things you could do:
1. put your server in a DMZ. Some problems there.
2. Use Citrix, logmein, gotomypc, or other to run a remote desktop from within the enterprise. This has proven moderately secure.
3. Open a hole in the corporate firewall. Good luck getting that through IT. Also, not very secure.
4. Go to n-tier architecture (i.e. a web or other application server). Put the app server in the DMZ.
I guess this is why Citrix, one of my least favorite pieces of software, is so popular.