If node 1 and node 2 are on the same server, rather than redirecting the browser, you might call the functions that would serve those URLs directly allowing them to return their results in response to the original request.

If node 1 or node 2 are on some other server, you could have your existing program (first.pm) submit the query and return the result to the browser. You could use LWP for this, or any other module that provides HTTP client functions.