In my case, I created a serverSocket at one device and a socket at the other.
When I change data to the client's database, I send a string at the server, saying what query to perform in order to have the 'server's' database updated.
On the other hand, when we update records at the 'server' side, we have a 'refresh' button at the 'client's' side which reads data from server and performs the needed query to update its database. I used a router to create this local network.
From what I see so far, it works, but I think what Erel suggested (mySQL approach) is the best practice.