Redirect Loop

This is what I might do:

iRule on site A VIP:

when HTTP_REQUEST {
    if { [URI::query [HTTP::uri] done] equals "1" } {
        HTTP::respond 302 Location "http://[HTTP::host]/default" "Set-Cookie" "SITEA=1;path=/"
    } elseif { not ( [HTTP::cookie exists SITEA] ) } {
        HTTP::respond 302 Location "http://www.bbb.com/communication"
    } 
}

Then in your site B link back to site A, add a "done=1" query string:

[a href="http://www.aaa.com/?done=1"]Click here to continue[/a]

On first request, the URI doesn't contain the done query string and the "SITEA" cookie doesn't exist, so redirect to site B. Clicking the link at site B issues a redirect back site A, which triggers an immediate redirect back to itself and setting the SITEA cookie. All subsequent requests should bypass both conditions.