redirect to new path

I think maybe you actually want to transparently rewrite and select pool based on incoming request rather than actually redirect (which sends a response to the client instructing it to re-request a new URL). Does this look like what you want (this assumes pl_pool has member 1.1.1.1:80 and pl_pool2 has member 2.2.2.2:80)?;-

HTTP_REQUEST { 
    Check the requested path   
   switch -glob [HTTP::path] { 
      "/site1/online/index.html"{ 
         HTTP::path "/online"
         pool pl_pool1 
      } 
      "/site1/online/authenticate.html"{ 
         HTTP::path "/online"
         pool pl_pool2 
      }       
   }
} 

Alternatively if you really do want to redirect this would be an option;

when HTTP_REQUEST {
    Check the requested path with wildcard matching
   switch -glob [HTTP::uri] {
      "/site1/online*" {
         HTTP::respond 302 noserver Location "/online?default"
         return
      }
     "/site1/online/authenticate.html"
      {
          HTTP::respond 302 noserver Location "/online?authenticate"
            return    
      }
      "/online?default"{
          HTTP::uri [HTTP::path]
          pl_pool1
       }
      "/online?authenticate"{
          HTTP::uri [HTTP::path]
          pl_pool2
       }
    }
}