In order to explore compatibility of good core plasma performance with divertor heat load mitigation, interaction between cold edge plasma and core plasma transport including edge transport barrier (ETB) has been analysed in the divertor detachment discharges of deuterium plasmas in LHD with RMP (resonant magnetic perturbation) field application. The RMP application introduces widened edge stochastic layer and sharp boundary in the magnetic field structure between the confinement region and the edge stochastic layer. The widened edge stochastic layer enhances impurity radiation and provides stable detachment operation as compared with the case without RMP. It is found that ETB is formed at the confinement boundary at the onset of detachment transition. However, as the detachment deepens resistive pressure gradient driven MHD mode is excited, which degrade the ETB. At the same time, however, the core transport decreases to keep global plasma stored energy (Wp) unchanged, showing clearly core-edge coupling. After gradual increase of density fluctuation during the MHD activity, spontaneous increase of Wp and recovery of ETB are observed while the detachment is maintained. Then the coherent MHD mode ceases and ELM like bursts appear. In the improved mode, the impurity decontamination occurs, and the divertor heat load increase slightly. Key controlling physics in the interplay between core and cold edge plasma is discussed. Comparison between deuterium and hydrogen plasmas show that the hydrogen plasmas exhibit similar features as the deuterium ones in terms of density and magnetic fluctuations, impurity decontamination toward higher confinement etc. But most of the features are modest in the hydrogen plasmas and thus no clear confinement mode transition with clear ETB formation is defined. Better global confinement is obtained in the deuterium plasmas than the hydrogen ones at higher radiation level.