Hi guys! Thank you for all your replies!
I have to admit it... I'm pretty lost

Following your advices and searching on the net I tried to better understand what's going on but I can't still figure it out...
Here's what I was able to understande:
An IRD application ([b]client#1[/b]) makes a call to a GVP application deployed on tomcat ([b]server#1[/b]).
The GVP application ([b]client#2[/b]) has to make a call to a [color=red][b]Web Service[/b][/color] (nginx, [b]server#2[/b]) via mutual authentication.
The communication between [b]client#1[/b] and [b]server#1[/b] is NOT in mutal authentication so I assume that the [i][b]clientAuth[/b][/i] parameter must be set to [i][b]false[/b][/i] on the server.xml file located in C:/Tomcat 7.0/conf/ since if set to true tomcat would wait for a certificate that do not exist (as a matter of fact if I call the RP where my IRD strategy is loaded on all I hear is a "beep" sound and no call to the GVP application is made).
Next, the communication between [b]client#2[/b] and [b]server#2[/b] has to be in mutual authentication. Client provided me with the (.p12) file. This file must be contained in the tomcat truststore, while the tomcat keystore must contain the tomcat certificate that it has to present to the [b]server#2[/b] (if I need to create this certificate or if it already exists is not clear because the environment is not managed by us, I will investigate). The certificate stored in the tomcat keystore MUST be contained in the [b]server#2[/b] trustore and the client authentication must be enabled in the nginx configuration... is that right?
Then, when and if everything will be set properly, what about Composer? Do I need to set the HTTPS Server Authentication section (as said by Renč) or the configuration made on tomcat would do the work?