The main website is SSL encrypted (which is why it starts
with https instead of http ).

However, when we link to YouTube through allvideos, a non-encrypted link is used. This
causes a warning in IE7 & IE8 about loading non-secure content from a secure
website.

Is there a work-a-round to this?

Here is a link:
www.soundfamilymedicine.com/joomla15/index.php?option=com_content&view=article&id=2&Itemid=10

The link is the same either you use or not AllVideos and has nothing to do with the message on IE9.