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The aim of this work is the development of a robust and accurate time integrator for the simulation of the dynamics of multibody systems composed by rigid and/or flexible bodies subject to frictionless contacts and impacts. The integrator is built upon a previously developed nonsmooth generalized-α scheme time integrator which was able to deal well with nonsmooth dynamical problems avoiding any constraint drift phenomena and capturing vibration effects without introducing too much numerical dissipation. However, when dealing with problems involving nonlinear bilateral constraints and/or flexible elements, it is necessary to adopt small time step sizes to ensure the convergence of the numerical scheme. In order to tackle these problems more efficiently, a fully decoupled version of the nonsmooth generalized-α method is proposed in this work, avoiding these inconveniences. Several examples are considered to assess its accuracy and robustness.