How to bypass load balancer in Weblogic?

I'm not a developer, I'm just tech support, but I am looking to help both my customer and our development team.  I am knowledgeable with Weblogic to my own needs for my job, but not too much beyond that, so this is a bit over my head.  Additionally I have spoken with our lead Java developer and he is perplexed as well.

Here are some highlights on what we've gathered so far and how the application is deployed.

We have deployed our software on a Weblogic cluster (it is our customer's server)
MachMS1 and MachMS2 are the servers involved here.
The software is only deployed onto MachMS1, i.e. we have used "Deploy to part of the cluster" option, no part of the software configuration is aware of MachMS2.
The deployment is a fully expanded folder
Our software utilizes the PD4ML library for Java

When PD4ML is invoked, according to the developer, we pass the document URL directly to the software.  I have been able to verify using the frontend for the software that accessing the software on MachMS1 is working OK, I do not get the same behavior as I do inside the software.

By looking at the access logs from the customer, I have been able to determine where the 404s are coming from (I get 404 errors sometimes).  The timestamps on MachMS1 and MachMS2 match.  Generation of the PDF files is yielding mixed results.  Less than 25% of the time, the PDF is generated successfully.  The other times, we get a PDF document in return, but, it prints out as a 404 error that Weblogic has spawned, not the page we're looking at.

The access logs show two requests, one to PD4ML, and the second (I presume) is to send the file back to the client.  On failures, the request is processed by MachMS2 - On successes, the request is processed by MachMS1.

Hopefully the above explains the situation somewhat; ultimately, my question is, how do we get this to always process on the same machine, and not pass any requests to the other machine?  We're not the only application on this server and naturally their admins are concerned about what potential impact global changes would have on the other applications.

I think maybe its trying to communicate to the load balancer for some of these requests, and the load balancer, functionioning normally, is happily spreading them between MachMS1 and MachMS2.  I don't know how or why though, our program was never made aware of the other server.

Due to technical reasons, we can not deploy our application on the MachMS2 server.  This has been proposed and rejected by the customer.

Is there something I can do (maybe with weblogic.xml file?) to sidestep the load balancer and make all the requests for our app flow through a single server?

I cannot be sure, but, I think on the first access for any of their applications, it is connecting to the load balancer and just maybe all subsequent requests are processed like this, so that even if we're calling the proper server and port right now, later on, it is not answering absolutely all the requests but spreading them, wherein the random 404's are popping up.

Weblogic 10.3 is the app server.

Thanks in advance