The directed flow of identified particles can serve as a sensitive tool for investigating the interactions during initial and final states in heavy ion collisions. This study examines the rapidity distribution (dN∕dydN∕dy), rapidity-odd directed flow (v1v1) and its slope (dv1∕dydv1∕dy) for π±π±, K±K±, p, and ˉpˉp in Au+Au collisions at different collision centralities and beam energies (√sNN=7.7√sNN=7.7, 11.5, 14.5, 19.6, 27, and 39GeV) using the UrQMD model. We investigate the impact of late-stage hadronic interactions on charge-dependent v1(y)v1(y) and its slope by modifying the duration of the hadronic cascade lifetime (ττ). The energy dependence of dv1∕dydv1∕dy for p (ˉpˉp) exhibits distinct pattern compared to π±π± and K±K±. Notably, we observe a change in the sign reversal position of proton dv1∕dydv1∕dy at different beam energies with varying ττ in central and mid-central collisions. Moreover, the difference in dv1∕dydv1∕dy between positively and negatively charged hadrons (Δdv1∕dyΔdv1∕dy) demonstrates a stark centrality dependence for different particle species. The deuteron displays a significant increase in dv1∕dydv1∕dy with increasing ττ compared to p and n. This investigation underscores the importance of considering the temporal evolution and duration of the hadronic phase when interpreting the sign reversal, charge splitting of v1v1 and light nuclei formation at lower RHIC energies.