Directional solidification is a common and important process in both scientific research and industrial practice. Dendrites are the most frequently observed microstructures in the directional solidification. It is known that dendrite coarsening in mushy zones is an unavoidable phenomenon that influences microstructures and thereby properties significantly. Moreover, the presence of temperature gradients during directional solidification leads to temperature gradient zone melting (TGZM), which yields dendrite arm migration towards higher temperatures. In the present work, the evolution of dendrite microstructures in the mushy zone during directional solidification is investigated through in situ experiments and cellular automaton (CA) simulations for a transparent succinonitrile-acetone (SCN-ACE) alloy. The phenomena of dendrite coarsening and the secondary dendrite arm migration toward high temperature direction due to TGZM have been observed by both experiment and simulation. Dendrite coarsening is found to be caused by three modes, including the remelting of small dendrite arms, and dendrite arm coalescence through the advancement of interdendritic grooves and joining of dendrite arm tips. The experimental measurements indicate that the average migration velocity of the secondary dendrite arm increases with increasing the temperature gradient. For a fixed temperature gradient, dendrite arm migration becomes slower with time. The experimental data agree reasonably well with the analytical predictions. The present CA model involving the mechanisms of both solidification and melting can effectively reproduce the typical features of secondary dendrite arm migration and dendrite coarsening as observed in experiments. The simulation results show that the local liquid concentrations near the lateral side of big arms and in the "valleys" between side arms are relatively higher than that at the tips of small arms. This drives solute diffusion and leads to the dissolution of small arms, the growth of thick arms, and advancement of interdendritic groove bases. However, at the groove between two relatively narrow and long adjacent side arms, the solute diffusion is obstructed. In this case, dendrite arm coalescence through joining arm tips together with an entrapped liquid droplet in the solid can be observed. The role of melting for microstructure evolution in mushy zones is investigated by comparing the simulation results using CA models with and without melting effect. It is demonstrated that remelting is one of the dominant mechanisms for dendrite arm migration and dendrite coarsening by the mode of small dendrite arm remelting. Moreover, remelting also promotes dendrite coarsening by the mode of dendrite arm coalescence.