Cache-enabled networks with multiple access (NOMA) integration have been shown to decrease wireless network traffic congestion and content delivery latency. This work investigates optimal power control in cache-assisted NOMA millimeter-wave (mmWave) vehicular networks, where mmWave channels experience double-Nakagami fading and the mmWave beamforming is subjected to beamsteering errors. We aim to optimize vehicular quality of service while maintaining fairness among vehicles, through the maximization of successful signal decoding probability for paired vehicles. A comprehensive analysis is carried out to understand the decoding success probabilities under various caching scenarios, leading to the development of optimal power allocation strategies for diverse caching conditions. Moreover, an optimal power allocation is proposed for the single-antenna case, for exploiting the cached data as side information to cancel interference. The robustness of our proposed scheme against variations in beamforming orientation is assessed by studying the influence of beamsteering errors. Numerical results demonstrate the effectiveness of the proposed cache-assisted NOMA scheme in enhancing cache utility and NOMA efficiency, while underscoring the performance gains achievable with larger cache sizes.