is it possible to redirect an URL www.siteA.com to www.site2.com/Default.aspx?SiteSource=siteA without changing the browser\'s URL?
Sim
You can also use mod_proxy (or similar functionality for a different web server) so that the page your server serves is the same as the remote page. But this has some security and performance implications (you're letting the client make your server do arbitrary work copying data across the network from the remote server).
server.transfer if on same server
If the URL doesn't change, it's not a redirect. However, you could create a proxy script that fetches the other page, rewrites any URLs within it, then outputs the result.
Use a HTML iframe to display www.site2.com/Page2.aspx?SiteSource=siteA, e.g.
<iframe src="www.site2.com/Page2.aspx?SiteSource=siteA" height="800" width="600" border="0" />
More about the iframe tag.