We present an analysis of the fast coronal mass ejection (CME) of 2012 March 7, which was imaged by both STEREO spacecraft and observed in situ by MESSENGER, Venus Express, Wind and Mars Express. Based on detected arrivals at four different positions in interplanetary space, it was possible to strongly constrain the kinematics and the shape of the ejection. Using the white-light heliospheric imagery from STEREO-A and B, we derived two different kinematical profiles for the CME by applying the novel constrained self-similar expansion method. In addition, we used a drag-based model to investigate the influence of the ambient solar wind on the CMEs propagation. We found that two preceding CMEs heading in different directions disturbed the overall shape of the CME and influenced its propagation behavior. While the Venus-directed segment underwent a gradual deceleration (from ~2700 km/s at 15 R_sun to ~1500 km/s at 154 R_sun), the Earth-directed part showed an abrupt retardation below 35 R_sun (from ~1700 to ~900 km/s). After that, it was propagating with a quasi-constant speed in the wake of a preceding event. Our results highlight the importance of studies concerning the unequal evolution of CMEs. Forecasting can only be improved if conditions in the solar wind are properly taken into account and if attention is also paid to large events preceding the one being studied.