We investigate the magnetic response of a superconducting Nb ring containing a ferromagnetic PdNi Josephson junction and a tunnel junction in parallel. Doubling of the switching frequency is observed within certain intervals of the external magnetic field. For sinusoidal current-phase relations in both junctions, our model of a double superconducting quantum interference device (a small two-junction loop that interrupts the larger ring) explains this feature by a sequence of current reversals in the ferromagnetic section of the junction in these field intervals. The switching anomalies are induced by the coupling between the magnetic fluxes in the two superconducting loops.