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Hybrid nanostructures consisting of two parallel InAs nanowires connected by an epitaxially grown superconductor (SC) shell recently became available. Due to the defect-free SC-semiconductor interface and the two quasi-one-dimensional channels being close by, these platforms can be utilized to spatially separate entangled pairs of electrons by using quantum dots (QD) in the so-called Cooper pair splitting (CPS) process. The minimized distance between the QDs overcomes the limitations of single-wire-based geometries and can boost the splitting efficiency. Here we investigate CPS in such a device where strong inter-dot Coulomb repulsion is also present and studied thoroughly. We analyze theoretically the slight reduction of the CPS efficiency imposed by the Coulomb interaction and compare it to the experiments. Despite the competition between crossed Andreev reflection (CAR) and inter-wire capacitance, a significant CPS signal is observed indicating the dominance of the superconducting coupling. Our results demonstrate that the application of parallel InAs nanowires with epitaxial SC is a promising route for the realization of parafermionic states relying on enhanced CAR between the wires. [ABSTRACT FROM AUTHOR]