At CRYPTO 2019, Gohr pioneered the application of deep learning to differential cryptanalysis and successfully attacked the 11-round NSA block cipher Speck32/64 with a 7-round and an 8-round single-key differential neural distinguisher. Subsequently, Lu et al. (DOI 10.1093/comjnl/bxac195) presented the improved related-key differential neural distinguishers against the SIMON and SIMECK. Following this work, we provide a framework to construct the enhanced related-key differential neural distinguisher for SIMON and SIMECK. In order to select input differences efficiently, we introduce a method that leverages weighted bias scores to approximate the suitability of various input differences. Building on the principles of the basic related-key differential neural distinguisher, we further propose an improved scheme to construct the enhanced related-key differential neural distinguisher by utilizing two input differences, and obtain superior accuracy than Lu et al. for both SIMON and SIMECK. Specifically, our meticulous selection of input differences yields significant accuracy improvements of 3% and 1.9% for the 12-round and 13-round basic related-key differential neural distinguishers of SIMON32/64. Moreover, our enhanced related-key differential neural distinguishers surpass the basic related-key differential neural distinguishers. For 13-round SIMON32/64, 13-round SIMON48/96, and 14-round SIMON64/128, the accuracy of their related-key differential neural distinguishers increases from 0.545, 0.650, and 0.580 to 0.567, 0.696, and 0.618, respectively. For 15-round SIMECK32/64, 19-round SIMECK48/96, and 22-round SIMECK64/128, the accuracy of their neural distinguishers is improved from 0.547, 0.516, and 0.519 to 0.568, 0.523, and 0.526, respectively.