Obla: I have multiple accounts on Outlook from AT&T, Gmail, Hotmail, Yahoo, etc., but I have never seen the behavior that you describe. In fact, I just tried to replicate that behavior by going offline and shutting down Outlook with non-Hotmail emails sitting in my Hotmail Outbox, but I couldn't replicate your problem.
The outgoing mail server for any particular email is determined by the outgoing mail server settings for account that particular email was sent "From:". If you compose a new email, then in the upper left of the email, you can select the "From" account. If, for example, that "From:" account is set to
Name@YadaYada.com AND if your outgoing mail server for that account is SMTP.YadaYada.com, then to my knowledge (and in my 15 years of using Outlook) that email will be sent from YadaYada.com's SMTP server.
Always. It would never be sent from
Name@Live.com or the Live.com outgoing mail server.
If you default data file is your Live.com account, then an email "From:"
Name@YadaYada.com might sit in your Live.com outbox on Outlook before going out. But it should actually be sent from the YadaYada.com mail server. (That's the way mine works.)
Are you sure that you're sending your emails "From:" the right account? You can set the default "From:" email account, but how you do that depends on your version of Outlook. It is worth noting that with older versions of Outlook (XP & 2003) when you composed a new email the default "From:" account would appear in the upper left of the email, and you could override that by selecting another account in the drop-down menu. I'm not sure about Outlook 2007 (which I skipped) but with Outlook 2010, that default "From:" account is typically, automatically overriden based on the emal account (Inbox, sent items, etc.) you're currently viewing at the time that you create a new email. (But you can override Outlook 2010's choice using the "From:" drop-down menu.) So in Outlook 2010, even if your default mail account is set to YadaYada.com, but you compose an email while viewing your Live.com Inbox, your "From:" box will show
Name@Live.com and your email will be sent from the Live.com servers unless you override the "From:" account.
As a somewhat related side note that may be of interest (although it doesn't solve your problem), only recipients who use Outlook will get the "sent on behalf of" notice. That's a safety feature that Microsoft built-into Outlook to help Outlook users avoid spoof-email scams. I don't know of any other email reader that provides such a notice.