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I'm not exactly sure I understand the your problem, so I'll try to restate it.
You're having trouble sending mail from your website to outside mailboxes, like hotmail and Yahoo. Is that correct?
If so, the first thing you'll need to check is whether or not you're hosted on a Linux server. If you're hosted on a Linux/Unix server, you'll need to check your setting under System Admin > Preferences > Mail Setup. If "PHP mail ()" is selected, and you can't send mail, try selecting "sendmail". You may have to contact your webhost so you can get the correct path to sendmail, but the defaults are usually correct.
If you're hosted on a Windows server, you'll need to select SMTP or SMTPAuth and provide an SMTP server, username, and password. If the only email account you have is Hotmail or Yahoo, you may have a problem there. Basically, you setup the XOOPS mail system for Windows the same way you would setup Thunderbird or Outlook.
Please let me know if I'm on the right track here.
JMorris