Firstly, make sure you have a secondary set of credentials linked to your account(Gmail, Facebook, psn). Next, log in with those credentials(specifically NOT your Xbox credentials). Unlink your Xbox credentials. Now, in your browser, clear your cache and cookies. What is probably happening is that your browser is autofilling your mother's hotmail information before you can fill in your own. After you've cleared your browser, attempt the linking process for your gamertag. This should resolve your problem.