The error, "553 sorry, that domain isn't in my list of allowed rcpthosts (#5.7.1)", means that you are trying to send email using the wrong smtp server.
Smtp related errors may have different numbers and slightly different wording, eg, "Relay access denied for...", but are all related to the same problem.
The smtp server that you use to send email is not determined by who hosts your email, but rather is a service of your Internet connection provider. All ISP's provide their customers with smtp servers, regardless of their email address.
One of the most important reasons for doing this is so spammers cannot connect to an unauthorized smtp server and use it to send mountains of spam. Occasionally, spammers find these "open" systems and flood them with mail. These systems are known as "open relays" and are the result of careless configuration by the operator.
Clients commonly see this error when they configure their PC at work, then try to use the same configuration at home, where the Internet connection is provided by a different ISP.
The fix for this situation is to change the smtp server in the mail client to match the one provided by the ISP..