Adam,
I think I might be close to solving this problem, at least in my case. I found an article on MySQL database replication here on phpBuilder and it's helped a lot. I would suggest taking a look at it.
As vincent suggested I will be running a MySQL database on the webserver as well as in the local shop. The local MySQL database will act as a master database and the webserver will act as a slave database. This means that the slave will update itself from the master and incorporate the changes into itself. The system then will be reversed so that the webserver also acts as a master and the local server acts as a slave. This way any changes in the webserver database will be automatically be sent to the local database. By doing this I will have some redundancy in the systems. If the webserver database goes down the store can operate normally and vice versa.
I know that sounds a bit complicated and I'm not even sure that it will work, but I'm going to test that out. I do see one very big problem with the above method though - data throughput. I think that the amount of data changing on a minute to minute basis will be too much to keep transmitting to the website. So the next paragraph explains my second alternative.
The website really only needs to know how much stock is in the store and not all the specific store related details of each and every product. So, I figure that I'll make a master/slave relationship in the store, with two databases running on the one server, but with the slave only updating the inventory amount of each item, not all the particulars. Then, I'll setup a master/slave relationship with the webserver to ensure that inventory amounts are kept up to date online and vice versa. This way the amount of data will be signifigantly minimized, yet will acheive the desired result of a combined inventory system.
I hope that makes sense and helps somewhat. If you've got any questions just post them and I'll try to explain it a bit better.
Devin