Inventory Control Across Multiple Servers .. Ideas?
I don't see the problem... You have an application running on one server that manages your database locally. There's no reason a remote server can't also talk to that database.
Of course, if you don't have a database and are instead using a homegrown app to act as some sort of faux-database, I recommend that you refactor to use something sort of actual DB sooner rather than later.
We currently have an inventory management system that was built in-house. It works great, and we are constantly innovating it. 
This past Fall, we began selling products directly on one of our websites via a Shopping Cart checkout.
Our inventory management system runs off a server in the office, while the three websites we currently have (only one actually sells things) runs off an outside source, obviously.
See my problem here? Basically, I am trying to think of ways I can create a central inventory control system that allows both the internal software and external websites to communicate so that inventory is always up to date and we are not selling something we don't have.
Our internal inventory tracking works great and flows well, but I have no idea on how I would implement a solid tracking system that can communicate between the two.
The software is all written in Python, but it does not matter as I am mostly looking for ideas and methods on how would this be implemented.
Thanks in advance for any answers, and I hope that made sense .. I can elaborate.