How to rewrite to another domain

I am trying to figure out how to "fake" a domain

For example..

http://www.mysite1.com works normally

http://www.mysite2.com works normally as well.

I want to be able to have people load: http://www.mysite1.com/FolderName/ and in the address bar they will see http://www.mysite2.com/FolderName 

Is this possible.

ITs basically to allow a sub site to use the checkout process on mysite1.com without them really knowing that they are on mysite1.com

The 2 domains are hosted on different servers.

mysite1 is IIS7 

mysite2 is wordpress on Godaddy

Thanks.