The Counterflow Dynamics Of Two Correlated Impurities In A Double Well Coupled To A One-Dimensional Bosonic Medium Is Explored. We Determine The Ground-State Phase Diagram Of The System According To The Impurity-Medium Entanglement And The Impurities' Two-Body Correlations. Specifically, Bound Impurity Structures Reminiscent Of Bipolarons For Strong Attractive Couplings As Well As Configurations With Two Clustered Or Separated Impurities In The Repulsive Case Are Identified. The Interval Of Existence Of These Phases Depends Strongly On The Impurity-Impurity Interactions And External Confinement Of The Medium. Accordingly The Impurities' Dynamical Response, Triggered By Suddenly Ramping Down The Central Potential Barrier, Is Affected By The Medium's Trapping Geometry. In Particular, For A Box-Confined Medium, Repulsive Impurity-Medium Couplings Lead, Due To Attractive Induced Interactions, To The Localization Of The Impurities Around The Trap Center. In Contrast, For A Harmonically Trapped Medium The Impurities Perform A Periodic Collision And Expansion Dynamics Further Interpreted In Terms Of A Two-Body Effective Model. Our Findings Elucidate The Correlation Aspects Of The Collisional Physics Of Impurities Which Should Be Accessible In Recent Cold-Atom Experiments.