First I woulld like you have a look at an installer
known as InstallAnyWhere. This is a multiplatform
installer.This should give you some idea of how you
can get your plugin into the webserver.
I also assume that the installer will install a JVM
for the specific platform  and also can do a Browser
side install in functionality like Flash plugin.
Regarding Applets:
Yes it is possible to connect to hosts other than the
origin. Have a look at "Digitally Signing Applets"
there are n-number of technical articles availble on
the net.
The other issues that has be sorted out here is how to
connect raw sockets from behind a firewall proxy (look
at Http Tunneling) and also how do you plan to run
your applet  when you
are in an network that does not support applets (this
is a very real scenario in the real world network
admins are very strumpy about opening sockets)

If you are thinking about some way to forward your
request to a java thread running on the server
side.You will have to look at ways through which you
can
1. Filter the request so that you know what request
has to be transoftmed into XML
2. How do I pass the request to the java thread?


Suggestion:

This application  looks like an ideal candidate to be
implemented as an webservice.

Have a look at SOAP and Webservices? Almost all
languages up to COBOL have some API that can access
Webservices?
Have a look at the AXIS SOAP server...

Implement a webservice on a remote  URL and use it as a
post man to forward request to other application
servers.On the client you will have SOAP Clients
written in their native languages..

like IIS will have asp SOAP clients,Apache may have
CGI/PERL, tomcat can have java SOAP clients etc etc

My understanding of your requirement may be wrong..so
if I make any silly suggesions I hope you will take it
in the correct sense