Are you running a clustered environment? Go to the QMC, Documents, Source Documents, check the QVW with the PDF distribution task, Distribute tab, Folder, and select the folder of Server 1. Note that the folder in Server 1 must be shared so it can be accessed from the account running the services as \\SERVER1\Folder
You should be able to publish a PDF document anywhere in the network, as long as the user account that runs the QlikView services has permissions on that folder to modify. The folder must be a network shared folder and you must set it up in the QMC as mentioned above, regardless it's a server or a particular user computer, as said, as long as the QlikView account has modify permissions on it.