Solution 1:

We've been using master<->master MySQL replication for 2+ years in production on critical databases without any issues. In our setup, databases are replicated over an unstable non-dedicated link. Configuration is easy and disaster recovery is without hassles. I recommend it.

Previously, we've been using a MySQL master->slave replication over a dedicated link with heartbeat for failing over, which is a viable option - but both machines have to be behind the same router.

Solution 2:

MySQL Cluster maybe?

Anyway, yeah, forget SQLite. It's the wrong solution for your problem.