How to sync two databases (alternative to mysql replication)?
mysqldbcompare, part of mysql utils, can check differences in structure and data among two servers. However, if you are making updates to one of the servers at the same time, this may not be enough.

pt-table-checksum and pt-table-sync, from Percona Toolkit, can respectively check and synchronise differences in data between a master and a slave in real time. It doesn't matter if both servers have different data, but it requires having the same tables with the same definition.

So probably you can use a combination of both. Both MySQL utils and Percona Toolkit are open source, freely downloadable and well established utilities among MySQL DBAs.