We discuss the adaptive full discretization of Gross-Pitaevskii equations with rotation term. The model suggests to use a Laguerre--Hermite spatial discretization in a method of lines approach. The resulting ODE system is propagated with higher-order splitting methods. Based on theoretical error bounds for this full discretization, asymptotically correct local error estimates employing either embedding formulae or the defect correction principle enable adaptive time-stepping which correctly reflects the solution behavior. Numerical examples illustrate the theoretical bounds and demonstrate the practical performance of the methods.