You need to call your ISP to learn how to access their local gateway while travelling.
To prevent spammers from sending mail through their email accounts, many ISPs do not allow mail to be sent through their mail servers unless directly connected to one of their dial-in gateways.
Can you receive from the "travel" computer while connected at home? If so, are you using the same ISP when traveling that you do when at home? Typically, you'll get that error when either the SMTP server address is not entered correctly in the email account settings or when using a different ISP connection that is not one of the domain email account.
SMTP servers are theoretically open so anybody could use them.
To avoid freeloaders they check the "From" field of the message you want to send against their list of approved users. If they don't find you there then it's rejected with a 550 error. (That happens to mean something else <g>)
Just check the "From" field of the messages that are working, and put the same info in corresponding fields of the new account (Tools/Accounts/Properties/General/User Information/EMail Address, I believe) Or better still copy the info from the same window in the old account.