I am a little bit confused about your problem here, so I am going to restate in a way that makes sense to me, then answer my version of your question. Please feel free to comment if I am not in line with what you are thinking.
You have a web application that uses a process-local memory cache for data. You want to expand to multiple nodes and keep this same structure for your program, rather than rely upon a 3rd party tool (memcached, Couchbase, Redis) with built-in cache replication. So, you are thinking about rolling your own using RabbitMQ to publish the changes out to the various nodes so they can update the local cache accordingly.
My initial reaction is that what you want to do is best done by rolling over to one of the above-mentioned tools. In addition to the obvious development and rigorous testing involved, Couchbase, Memcached, and Redis were all designed to solve the problem that you have.
Also, in theory you would run out of available memory in your application nodes as you scale horizontally, and then you will really have a mess. Once you get to the point when this limitation makes your app infeasible, you will end up using one of the tools anyway at which point all your hard work to design a custom solution will be for naught.
The only exceptions to this I can think of are if your app is heavily compute-intensive and does not use much memory. In this case, I think a RabbitMQ-based solution is easy, but you would need to have some sort of procedure in place to synchronize the cache between the servers on occasion, should messages be missed in RMQ. You would also need a way to handle node startup and shutdown.
Edit
In consideration of your statement in the comments that you are seeing access times in the hundreds of milliseconds, I'm going to advise that you first examine your setup. Typical read times for a single item in the cache from a Memcached (or Couchbase, or Redis, etc.) instance are sub-millisecond (somewhere around .1 milliseconds if I remember correctly), so your "problem child" of a cache server is several orders of magnitude from where it should be in terms of performance. Start there, then see if you still have the same problem.