Using the drone as a cooperative relay (CR) can improve the connectivity of Internet of Vehicles (IoV) on highways in remote areas. Meanwhile, considering limited spectrum resources, non-orthogonal multiple access (NOMA) is regarded as a promising approach for increasing spectrum efficiency and the channel capacity of IoV. Motivated by the above, this paper investigates the application of the cooperative relaying system (CRS) and NOMA in drone-enabled IoV. Specifically, we propose a NOMA-enhanced CRS in drone-enabled IoV for spatially multiplexed transmissions, where the base station is allowed to transmit two different data symbols simultaneously to associated vehicles. Next, in order to analyze the capacity, we adopt the incomplete Gamma function and Taylor expansion of Bessel function to derive the closed-form expression of average data rates. Then, to simplify the calculation, we provide an approximate expression by using the Gauss-Chebyshev integral. Afterwards, to fully exploit the advantages of the CR, the CR height is optimized by employing the Steffensen method, which has second-order convergence without calculating the derivative. In order to apply to real scenarios, we extend the considered model to accommodate large-scale networks by using the stochastic geometric method. Finally, the simulation results show the accuracy of the obtained approximate results, where the performance gap is 1.6%. Moreover, the NOMA-enhanced CRS using the proposed CR height optimization scheme outperforms the current works in terms of the sum data rate. Furthermore, utilizing the Steffensen method can reduce the running time by 26.3% in comparison with the Newton method.