Windows Live mail

I originally had a Hotmail account, then when I went to Windows 7  I started using the Windows Live email.  So this Windows Live pulls in the soandso@hotmail.com emails just fine.  Then I added another email account for business that is a *** Email address is removed for privacy *** account.  The problem is even though I made the business email (which was added second) the "primary" alias in Windows Live account, every time I send an email from business it arrives with the personal email address as the sender.  Can anyone tell me how to fix this without having to delete my original personal email address?  I thought that was the whole idea to have "aliases", was to manage different email addresses in one place.  But peoples receiving my business email say that it shows it came from my other alias address and they don't know/realize it's from my business.