We give a rigorous error analysis for the full discretization of Gross-Pitaevskii equations with rotation term. The model describes rotating Bose-Einstein condensates. The spatial discretization uses a spectral method based on Laguerre-, Fourier- and Hermite functions and the time integration is realized by high-order split-step methods. We give a rigorous analysis of the discretization error and moreover discuss practical aspects of adaptive step-size choice based on local error estimation.