To provide security to all pairs of nodes in network mobility (NEMO) while executing the handoff between different technologies, a hybrid cryptosystem with a suitable network selection mechanism is proposed. All pairs of nodes, i.e., Mobile Node (MN), Mobile Router (MR), Correspondent Node (CN) and MN, and Home Agent (HA), respectively, are considered. A proper security mechanism is proposed to provide confidentiality to Bound Update (BU) during handoff and conversation between MN, MR, and HA using the elliptic curve cryptography (ECC). In this solution, a network selection mechanism is proposed based on user preference and Received Signal Strength (RSS) in a heterogeneous network. The proposed model can protect the communication using security analysis from all NEMO standard attacks. Whenever NEMO moves, MR intimates to HA about the address change using (BU) and MR receives Binding Acknowledgement (BA) as a reply. During data (frame) exchange and registration between MN, CN, and HA, various security threats arise. In the earlier work, only the security solution is given, and the best network selection algorithm is not provided in a heterogeneous environment. Therefore, in this paper, the best network selection is contributed based on Received Signal Strength (RSS) and user preferences. A comparison of the proposed model is drawn with Return Routability Procedure (RRP). Authentication is provided for communication between MN and CN. The proof is derived using BAN logic. Many standard security attacks have been successfully avoided on all pairs of communications. It has been observed that the proposed model achieves 2.4854% better throughput than the existing models. Also, the proposed model reduces the handoff latency and packet loss by 2.7482% and 3.8274%, respectively.