SQL Server Distributed Availability Group Usage Pattern
The documentation for Distributed availability groups states:


  Although each underlying availability group of the distributed availability group has a listener, a distributed availability group has no listener.


So there is no way for a client to connect to a distributed AG because there is no listener for it.  Clients must connect to the listener of the AG that is currently the primary.

In order to fail over a DAG and provide connectivity for clients, you would need to initiate failover on the DAG, and then create a listener on the DR cluster with the same name as the current listener that clients connect to.

If you are using Enterprise edition, creating a DR node in the cluster and making it an asynchronous replica in the regular availability group is usually a better option, so if you haven't considered that I recommend looking into it.