All-wheel-independent-drive electric vehicles (AWID-EVs) have considerable advantages in terms of energy optimization, drivability and driving safety due to the remarkable actuation flexibility of electric motors. However, in their current implementations, various real-time data in the vehicle control system are exchanged via a controller area network (CAN), which causes network congestion and network-induced delays. These problems could lead to systemic instability and make the system integration difficult. The goal of this paper is to provide a design methodology that can cope with all these challenges for the lateral motion control of AWID-EVs. Firstly, a continuous-time model of an AWID-EV is derived. Then an expression for determining upper and lower bounds on the delays caused by CAN is presented and with which a discrete-time model of the closed-loop CAN system is derived. An expression on the bandwidth utilization is introduced as well. Thirdly, a co-design based scheme combining a period-dependent linear quadratic regulator (LQR) and a dynamic period scheduler is designed for the resulting model and the stability criterion is also derived. The results of simulations and hard-in-loop (HIL) experiments show that the proposed methodology can effectively guarantee the stability of the vehicle lateral motion control while obviously declining the network congestion.