We present a coarse-grained (CG) model of a charged double-stranded DNA immersed in an electrolyte solution that can be used for a variety of electrokinetic applications. The model is based on an earlier rigid and immobile model of Weik et al. and includes now semi-flexibility and mobility, so that DNA dynamics can be sufficiently captured to simulate a full nanopore translocation process. To this end we couple the DNA hydrodynamically via a raspberry approach to a lattice-Boltzmann fluid and parametrize the counterions with a distant dependent friction. The electrokinetic properties of the CG DNA model inside an infinite cylinder is fitted against experimental data from Smeets et al. and all-atom simulation data from Kesselheim et al. The stiffness of our CG DNA is modeled via a harmonic angle potential fitted against experimental data of Brunet et al. Finally, the quality of our tuned parameters is tested by measuring the electrophoretic mobility of our DNA model for various numbers of base pairs and salt concentrations. Our results compare excellently with the experimental data sets of Stellwagen et al. and Hoagland et al.