I suspect it isn't working because you're $mech->geting $url2. I don't think you want to do that - after you've POSTed with $mech->click, $mech's "current url" ($mech->uri) will change. Try removing the line $mech->get($url2); and see if it works.

I can see a few other problems with your code:

• You don't need to use LWP::UserAgent; WWW::Mechanize is a subclass of it which means it use it for you.
• Don't think you need to use HTTP::Cookies either; I can do $mech->cookie_jar(HTTP::Cookies->new()); only using WWW::Mechanize.