The Coulomb correlation and quantum coherence in a double-dot Aharonov-Bohm interferometer can result in two distinct transport channels: a fast channel and a slow one, while their coupling is tunable by changing the magnetic flux passing through an interference loop. However, these effects cannot be manifested by the conventional transport current. In this work, employing the large-deviation method which was originally developed in the nonequilibrium statistical mechanics, we perform a large-deviation analysis for the transport through this double-dot interferometer system and reveal a clear dynamical phase transition behavior.