In many variational formulations of the shallow-water equations, centrifugal effects are absorbed into the gravitational potential. In the small-scale rotating tank setting, this approximation is not made. This work considers the one dimensional version of the rotating sloshing tank problem. We derive equations of motion for a two-layer inviscid shallow-water sloshing problem with prescribed bottom topography, formulated in a rotating frame. The derivation follows the Lagrangian approach of Dellar and Stewart [2], specialised to one dimension and retaining all terms. An alternative derivation is obtained following the approach of Alemi Ardakani and Bridges [4] extending the theory to a multilayer problem. The equations admit a non-canonical Hamiltonian formulation, extending the multilayer framework. A corresponding Poisson bracket is derived, consistent with the geometric and conservation structure of the continuous equations. A structure-preserving discretisation within the Dellar and Stewart [1] framework yields exact conservation of mass and energy at the semi-discrete level. The resulting numerical scheme retains antisymmetry of the discrete Poisson bracket and exhibits no secular drift in the conserved quantities over long-time integrations spanning many sloshing periods. Comparisons with non-symplectic time integration schemes highlight the essential role of symplectic temporal discretisation in maintaining invariants and numerical stability in long-time simulations. REFERENCES [1] Dellar, P., Stewart, A. L., An energy and potential enstrophy conserving numerical scheme for the multi-layer shallow water equations with complete Coriolis force, Journal of Computational Physics, Vol. 313, pp. 99–120, 2015. [2] Dellar, P. J., Salmon, R., Multilayer shallow water equations with complete Coriolis force. Part I: Derivation on a non-traditional beta-plane, Journal of Fluid Mechanics, Vol. 651, pp. 387–413, 2009. [3] Holm, D. Hamiltonian structure for two-dimensional hydrodynamics with nonlinear dispersion Physics of Fluids, Vol. 31, pp 2371–2372. 1988. [4] Alemi, H. A. and Bridges T. J. Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in three dimensions Journal of Fluid Mechanics, Vol 667, pp 474–519 2011