How to keep two MySQL databases in sync?
Here's a quick reference of MySQL Replication by @Mark Baker or you can use MySQL Workbench Synchronization.
So I finally found a solution to my problem. Since this was an issue for WordPress I found two plugins that worked really well.
Free one: Database Sync
Very simple and has an easy push/pull interface.
Paid Plugin $40-200: WP Migrate DB Pro
Much more polished and has an option to select specific tables you want to sync.
There's an answer to the duplication problem here. However, that's only the start of your difficulties. If two people are making changes independently to two copies of one database, merging the two will inevitably cause nightmares. In short, yes there will be merge conflicts. Exactly what, and what you do about it, will depend on the nature of the changes each of you have made. Good luck!