This paper investigates the formation reconfiguration problem of wheeled mobile robot (WMR) systems under spatiotemporal and input constraints. Specifically, we formally introduce the concept of fixed-time discrete control Lyapunov functions (FT-DCLFs) and provide the control Lyapunov constraint condition that ensures the fixed-time stability of discrete-time systems. We then consider the design of an integrated control strategy that confines the trajectories of WMR systems to a safe set (avoiding collisions) and steers them to the goal state within a fixed time. To this end, we utilize a quadratic programming (QP) formulation to compute the control inputs by unifying the discrete-time control barrier function (DCBF) and FT-DCLF within the framework. Furthermore, we implement the proposed algorithm through simulation studies on the formation reconfiguration of WMRs in environments with obstacles.