Alcohol-related driving remains a significant concern due to its profound association with the likelihood of traffic crashes and the severity of resulting injuries, especially between two vehicles. To investigate the determinants influencing the alcohol-related two-vehicle crash severity, a foundational framework employed was a multinomial logit model. Meanwhile, by incorporating random intercept from individual case and vehicle levels to accommodate unobserved heterogeneity, and covariance matrices to underscore correlated outcomes, a multivariate hierarchical random parameters correlated outcomes logit model was proposed. Additionally, to further explore the potential temporal instability of explanatory variables, a random slope from a per-year indicator was introduced into the model. Crash data from the US Statewide Integrated Traffic Records System (SWITRS) database spanning from January 1, 2016, to December 31, 2021, was used. Three crash injury severity categories were examined, encompassing severe injury, minor injury, and no injury, with characteristics related to the driver, vehicle, road, environment, crash, and time serving as explanatory variables. The model results highlighted significant heterogeneity, with each case and vehicle accounting for 56.9% of the total variance for minor injuries and 50.8% for severe injuries. Furthermore, a significant negative correlation was explicitly exhibited between minor injury and severe injury outcomes at the case level. In terms of potential temporal instability, we provided per-year (2016–2019) parameter estimates and identified significant instability for indicators such as non-intersection, broadside and head-on collisions, cloudy weather conditions, and drivers who had been drinking but were not under the influence. Considering the impact of the COVID-19 pandemic, we divided the accident time into pre-COVID and during-COVID periods, modeling parameter estimates for both periods. This analysis revealed significant instability in several factors influenced by the pandemic. Additionally, noteworthy disparities in the estimated results of explanatory variables emerged in comparison to those general two-vehicle crashes or alcohol-related crashes, providing valuable insights. For instance, drivers who had been drinking but were not under the influence were less likely to sustain severe injuries, but the probability of minor injuries increased. These findings underscore the significance of thorough investigations into the determinants of injury severity in alcohol-impaired two-vehicle crash severity, along with the temporal instability of such factors. They hold important implications for effective traffic safety management and the formulation of prohibitive countermeasures.