Question on Connected Tables

Our company has several apps, it has become apparent to me that we have a lot of common information in tables across these apps.  It has also become apparent that we could leverage connected tables to help manage this, so that we only need to update a table in one app as opposed to updating the same information in several apps.

I'm wondering though how one would handle the existing table relationships.  Example.  We have an app (App A) that has a 'Customer' table.  This table could be used in another app (App B) which has it's own 'customer' table.  But the second app's table has several existing child tables.  

Would I be able to just make a new connected table from App A to App B, and then just sever the existing relationship with one of App B's child tables (but keep the reference field), then make a new relationship with the connected table?  That seems possible to me, but I'm wondering about the key field in the connected table.  I wouldn't be able to use the key field the source table is using because in App B the 'Customer' table uses a calculated key.  Would I be able to define a new key field in the connected table so that the child table keys could be mapped to it?