a database trigger is hardly a place where one should attempt to connect to another database (in not connected already)... why do you want to hard-link the two systems, what if the other database is down, is your write trigger return an error and roll-back everything?
that's definitively the approach you want to take for data replication/synchronization... the source system should probably work just fine when the target is down for some reason, it will have to catch-up when the target system gets back online but the synchronization task is not something that should bother the application running on the source database.
just write some audit logs in a replication table in the source database, that can be done in replication triggers, and then have some batch processing do the real replication.