The third VDB treats other two VDBs as two separate sources. However, you can import the first two VDBs into third VDB and use same translator name and JNDI name for source, then it will treat as your expectation in (a)
I've attempted to update the connection profile for the first two VDBs but I'm unable to do so because the models are 'read-only'. I'm using Designer 9.0.1 with server 8.8 in Eclipse 4.4.2.
Anyhow, to work around, I created a VDB with the two views and imported each individually as its own VDB source model. So the connection profile info is the same on both source models now. However, I'm still not seeing the filter get pushed down to the database. Do you think the coalesce function is causing issue and Teiid doesn't know how to map that back to each VDB as a filter?
coalesce(vdb_a.key, vdb_b.key) as key
The behavior I explained is for server. Designer, does help you create "import" VDB part during the (third) VDB creation, but when you do preview it will NOT use the same semantics as server. BTW, when I say import, it means Teiid Designer User Guide
As per the specific issue of coalesce, you would need to see query plan for the reason.