The coupling magnet for the Muon Ionization Cooling Experiment has a self-inductance of 592 H and the magnet stored energy of 13 MJ at a full current of 210 A for the worst operation case of the MICE channel. During a quench, the stored energy and the high conductor current density will cause a large temperature rise and induce considerable impact of stresses. One test coil was built in order to validate the design method and practice the stress and strain situation which occurs in the coupling coil. In this study, the analysis on stress redistribution in the sub-divided winding during a quench was performed. The stress variation may bring about failure of epoxy resin, which is the cause of a new normal zone arising. Spring model for impregnating epoxy and fiber-glass cloth in the coil was used to evaluate the mechanical disturbance by impregnated materials failure. This paper presents the detailed dynamic stress and stability analysis to assess the stress distribution during the quench process and to check whether the transient loads are acceptable for the magnet.