Why not just use the web interface for GMail and your other account?

If that doesn't work for you, can you give a clearer picture of what you want to be able to do?

This may give you some ideas:
http://lifeofelling.blogspot.com/2006/05/lambi-pooch-using-gmail-for-work.html

I'm totally confused by your explanation. Could you pls clarify?

This may completely solve your problem if your company's firewall/routers are configured in the typical way.

I. The Problem
Large organizations typically block SMTP mail sending (port 25) from inside their networks as a way to prevent rogue user spam and email virus propagation.

II. The Solution!
Since port 25 will not work, we simply have to find another port. Unfortunately, this depends on your mail provider. However, Apple's .Mac service and many others offer (typically without documentation) SMTP that requires a login on port 587. Setting this up is easy:

1. Open Mail.app.
2. Click the application menu (labeled "Mail") then choose "Preferences."
3. Click the "Accounts" icon.
4. Select the account you wish to change in the "Accounts" list on the left of the preferences window.
5. Verify that the "Account Information" tab is the one you are viewing.
6. Click the "Server Settings. . ." button near the "Outgoing Mail Server (SMTP)" label.
7. Change the "Server port" option from the current value (normally 25) to 587.
8. Verify that "Use Secure Sockets Layer (SSL)" is checked (it is not by default).
9. Choose the option "Password" from the "Authentication" drop-down menu.
10. Enter your user name and password if it is not automatically filled in for you.
11. Click "OK."
12. Close the preferences window.
13. Quit and Reopen Mail.

III. Possible Problems
Those settings are right on for .Mac accounts. Other mail providers may need other option settings, but, in my experience, the only thing to change if you have problems is the SSL checkbox. Otherwise, it is likely that your mail provider does not offer service on an alternate port.