Initializing Transactional Replication From two Different Database Backup
The replication topology that you are describing is known as the Central Subscriber Model which is comprised of two or more Publishers replicating to one Subscriber.  The dilemma you are having is how to go about initializing the Central Subscriber, which is a common conundrum.

I have talked about this in detail in my post Central Subscriber Model Explained and have found through experience that the best way to initialize a Central Subscriber is with a snapshot, utilizing horizontal partitioning, static row filters, and setting the Action if name is in use article properties to Delete data. If article has a row filter, delete only data that matches the filter.

If you have anymore questions please let me know.  I hope this helps.