Well, it would be nice if it were simple. =/
However, to my knowledge, there is no way to just modify your open()s to work like this.
In order to get that file, you'll need to transfer it over the network through standard methods. The options that come immediately to mind are ftp or cvs (cvs would be my choice in this case). There are modules to help you with either one. Both cases would require you to get the file, modify it, and send back the new version.
Keep in mind with using ftp, you may very well need to implement locking of some sort to keep the files in sync.

But this is a quick-fix type solution. A brute method.
IMO, this doesn't seem to be a situation in which load balancing is ideal. Perhaps it should be considered that only one of these servers be used to host the data file.

In my experience, it has been more trouble than it's worth to keep mirrors of constantly changing data on seperate servers.
Well anyway, sorry if this isn't what you were looking to hear. </my two cents>