Help with rewriting the URI

Well, it looks like you're almost there. The only thing you need to add now is the logic around the HTTP::uri command to change the uri as desired. If you're looking to change all Internal pool request URIs to /int/intsearch and all external request URIs to /ext/extsearch, you'd want something like:

redirection_acl_rule
this event is triggered when a client - BIPIP TCP connection is established
when CLIENT_ACCEPTED {
  is client IP address defined in the trusted datagroup?
  if { [matchclass [IP::client_addr] equals $::trusted_datagroup] } {
    HTTP::uri /int/intsearch
    pool Internal_7008_Pool
  } else {
    requests that did not match the conditions redirect to the External search
    HTTP::uri /ext/extsearch
    pool External_7006_Pool
  }
  log the client IP address -> destination IP address
  log local0. "request accepted from client: \
  [IP::client_addr] -> [IP::local_addr]"
}

If you only wanted this done if they had no requested URI or a URI of "/", then you'd need some additional logic:

when CLIENT_ACCEPTED {
  is client IP address defined in the trusted datagroup?
  if { [matchclass [IP::client_addr] equals $::trusted_datagroup] } {
    if{ [string length [HTTP::uri] <= 1 } { 
      HTTP::uri /int/intsearch
    }
    pool Internal_7008_Pool
  } else {
    requests that did not match the conditions redirect to the External search
    if{ [string length [HTTP::uri] <= 1 } { 
      HTTP::uri /ext/extsearch
    }
    pool External_7006_Pool
  }
  log the client IP address -> destination IP address
  log local0. "request accepted from client: \
  [IP::client_addr] -> [IP::local_addr]"
}

HTH,

Colin