We present ARC2 (Astrophysically Robust Correction 2), an open-source python-based systematics-correction pipeline, to correct for the Kepler prime mission long-cadence light curves. The ARC2 pipeline identifies and corrects any isolated discontinuities in the light curves and then removes trends common to many light curves. These trends are modelled using the publicly available co-trending basis vectors, within an (approximate) Bayesian framework with 'shrinkage' priors to minimize the risk of overfitting and the injection of any additional noise into the corrected light curves, while keeping any astrophysical signals intact. We show that the ARC2 pipeline's performance matches that of the standard Kepler PDC-MAP data products using standard noise metrics, and demonstrate its ability to preserve astrophysical signals using injection tests with simulated stellar rotation and planetary transit signals. Although it is not identical, the ARC2 pipeline can thus be used as an open-source alternative to PDC-MAP, whenever the ability to model the impact of the systematics removal process on other kinds of signal is important.