How to direct HTTP request to a particular pool member and keep the persistence (cookie insert mode)

Do you have a cookie persist profile on the virtual server?

It would probably be best to have the cookie persist profile on the virtual server (if you don't already), and then change your rule slightly. You shouldn't need the "persist cookie insert cookiemonster" line that you currently have at all. Instead you'll want to add "persist none" in the else part of your if:

   ...
      HTTP::uri "/$newuri"
       Remove this persist command since it is already defined on the virtual
      pool testpool member $myserverip 80
   } else {
      pool testpool
      persist none
   }
}