I'm setting up a medical server for a hospital that has doctors located in 3 different locations, meaning there would be 3 servers (1 in each location). All 3 servers would just have the following software:

Ubuntu Server 12.04 minimal
MySQL, PHP 5, Apache
The medical software which would read/write to the MySQL database
Remote admin apps like Nagios & Webmin
Rsync for backup (rsync-over-ssh) as a cron job

and the doctors at each location would access patient & billing data from their respective servers.

What I'd like is, that each of these servers all have synchronized info (especially the mySQL database's) - let's say on an hourly basis each of these servers synchronize data to a common remote server and the data is then brought down to each of the servers.

I know an easier way would be to have the medical app running on a remote web server, but since this is medical that we're talking about and knowing how common it is in our area for the net to go gown, I wouldn't like a web based scenatio.

Is such a setup possible? Would this be the right way to do things or is there a better way to this?

Would really appreciate views and comments (or how to set this up) on this.