DNS Suffix on two network Interfaces on MacBook Pro
The problem that you are having is that you have two separate networks with their own DNS that don't know about each other - .intern and .home.  

The problem comes in when you try to ping a host on a network (whichever is primary; let's assume .home) to another network (.intern).  It will fail because the DNS for .home knows nothing about the .intern domain.  It will assume the request needs to be forwarded to the ISP's DNS; and they don't know about that domain either.

You can fix this by enabling Unbound DNS resolver on your Mac so it can query itself. You will need to configure it to perform a split-horizon DNS service.  Then, set your Mac to query only itself for DNS lookups.

Basically, your Mac becomes a DNS server that's aware of both networks and will respond to its DNS queries accordingly.