The latest evolutionary phases of low- and intermediate mass stars are characterized by complex physical processes like turbulence, convection, stellar pulsations, magnetic fields, condensation of solid particles, and the formation of massive outflows that inject freshly produced heavy elements and dust particles into the interstellar medium. By investigating individual objects in detail we wish to analyze and disentangle the effects of the interrelated physical processes on the structure of the wind forming region around these objects. We use the Northern Extended Millimeter Array (NOEMA) to obtain spatially and spectrally resolved observations of the semi-regular Asymptotic Giant Branch star RS Cancri to shed light on the morpho-kinematic structure of its inner, wind forming environment by applying detailed 3-D reconstruction modeling and LTE radiative transfer calculations. We detect 32 lines of 13 molecules and isotopologs (CO, SiO, SO, SO_2_, H_2_O, HCN, PN), including several transitions from vibrationally excited states. HCN, H^13^CN, millimeter vibrationally excited H_2_O, SO, ^34^SO, SO_2_, and PN are detected for the first time in RS Cnc. Evidence for rotation is seen in HCN, SO, SO_2_, and SiO(v=1). From CO and SiO channel maps, we find an inner, equatorial density enhancement, and a bipolar outflow structure with a mass loss rate of 1x10^-7^M_{sun}_/yr for the equatorial region and of 2x10^-7^M_{sun}_/yr for the polar outflows. The ^12^CO/^13^CO ratio is measured to be ~20 on average, 24+/-2 in the polar outflows and 19+/-3 in the equatorial region. We do not find direct evidence of a companion that might explain this kind of kinematic structure, and explore the possibility that a magnetic field might be the cause of it. The innermost molecular gas is influenced by stellar pulsation and possibly by convective cells that leave their imprint on broad wings of certain molecular lines, such as SiO and SO. RS Cnc is one of the few nearby, low mass-loss-rate, oxygen-rich AGB stars with a wind displaying both an equatorial disk and bipolar outflows. Its orientation with respect to the line of sight is particularly favorable for a reliable study of its morpho-kinematics. The mechanism causing early spherical symmetry breaking remains however uncertain, calling for additional high spatial and spectral resolution observations of the emission of different molecules in different transitions, along with a deeper investigation of the coupling among the different physical processes at play.