I mean like, some program/script that takes the ip+login for the two dbs, and goes through them looking for changes, and edits the second when it finds them.
Yep that is exactly what is needed - and you are in charge - it has no way to know what databases, tables and columns to iterate. There are likely many fields you don't want updated from server to server (metadata).
(which is exactly what Altrea told you in the first place)
THERE IS such a thing as slaves and mirrors, but they are meant to be unconditional replicants. they are for redundancy/failover by design, not selective updating.'
Google this - "MySQL slaves mirrors"