Trigger on replicated DB
It looks like replication is what you need here. There are different flavors of replication (merge, transactional and snapshot) that are suitable in different situations. In this case, it looks like transactional replication is what you need, unless changes on the secondary copy have to be propagated to the original copy of the data.

I fail to understand the role of the second schema. If you need both schemas at the primary database, then trigger could be a way to keep the two schemas in sync. If you need the second copy of the tables only at the second server, you can replicate the tables from sch1 to sch2 without issues.