merging two irules into one efficient one.

So maybe something like this?

when HTTP_REQUEST {

    Check if the Host is www.mysite.com
   if { [string tolower [HTTP::host]] eq "www.mysite.com"} { 

       Rewrite the Host header to www.mynewsite.com
      HTTP::header replace Host "www.mynewsite.com" 

   } else {

       look for the second string in the data group and redirect 
      set newURI [findclass [HTTP::uri] $::newURI-Datagroup " "] 
      if { "" ne $newURI } { 
         HTTP::redirect "https://www.mynewsite.com$newURI" 
      } else {
         HTTP::redirect "https://[HTTP::host][HTTP::uri]" 
      }
   }
}

If you're having issues with the redirects, can you post an anonymized copy of the datagroup contents from the bigip.conf? Please also note a couple of URIs which do and don't work.

Aaron