In this paper, we analyze the Kang-Park and ESS-FH scheme, and propose an Enhanced Secure-Mobility Data Management Scheme for FPMIPv6 (ESS-FP). Based on the CGA method and public key Cryptography, ESS-FP provides a strong key exchange and key independence, in addition to improving the weaknesses of Fast Handover for Proxy Mobile IPv6 (FPMIPv6). We formally verify the proposed scheme based on BAN (Burrows, Abadi, and Needham) Logic, and analyze and compare its handover latency with those of the Kang-Park scheme and ESS-FH. In addition, we propose an inter-domain fast handover scheme for PMIPv6, using the proxy-based FPMIPv6. Furthermore, we apply an Enhanced Secure-Mobility Data Management Scheme for FPMIPv6 in the Internet of Things (IoT) environments.