As long as the backend servers are running both host applications and accept both domains then you can modify the Host header with
HTTP::header replace "Host" "www.host2.com"
This will effectively change the host header to effectively change the url from
http://www.host1.com/foo to
http://www.host2.com/foo. You can also use the "HTTP::uri" command to modify the URI that is sent to the backend server.
HTTP::uri "/path2"
This would change the request from
http://www.host1.com/path1 to
http://www.host1.com/path2.
A redirect is typically needed if control needs to be passed to a resource outside the scope of the proxy.
If this doesn't give you enough of what you need, if you can specify exactly what you want the BIG-IP to do (ie, all inputs and all outputs and where the output is to go) I can try to get you something more concrete.
-Joe