We illustrate how macroscopic rotations can be utilised to trigger and control a spin dynamics within the ground doublet of both Kramers and non-Kramers-type molecular nanomagnets via the non-Abelian character of the time-evolution operator. For Kramers magnets, we show how this effect can be harnessed to realise single-qubit quantum gates and give the explicit example of a recently reported CoCl2(tu)4 single-molecule magnet (SMM). We demonstrate that gating operations could be performed on this magnet in as fast as 10 ps before the breakdown of adiabaticity, much faster than typical spin-lattice relaxation times. Based on this effect, we also suggest CoCl2(tu)4 as a quantum gyroscope for sensing yaw-axis rotations. For integer spin nanomagnets where non-axial crystal field interactions often lift ground state degeneracy, we show how spin dynamics from the non-Abelian geometric propagator can be recovered using non-adiabatic macroscopic rotations not-necessarily resonant with the tunnel splitting gap. Using the well-known TbPc2 single-ion magnet as a further example, we identify an experimentally plausible non-adiabatic rotation that induces a coherent superposition of tunnelling ground states, tantamount to preparing each member of a TbPc2 ensemble in the maximal angular momentum state |mJ = 6〉. The detection of an ensuing coherent oscillation of the macroscopic magnetisation polarised along the TbPc2 principal magnetic axis after the completed rotation could then proceed via time-resolved magnetisation measurements.