Automatic license plate recognition (ALPR) and vehicle make and model recognition underpin intelligent transportation systems, supporting law enforcement, toll collection, and post-incident investigation. Applying these methods to videos captured by handheld smartphones or non-static vehicle-mounted cameras presents unique challenges compared to fixed installations, including frequent camera motion, varying viewpoints, occlusions, and unknown road geometry. Traditional ALPR solutions, dependent on specialized hardware and handcrafted OCR pipelines, often degrade under these conditions. Recent advances in large vision-language models (VLMs) enable direct recognition of textual and semantic attributes from arbitrary imagery. This study evaluates the potential of VLMs for ALPR and makes and models recognition using monocular videos captured with handheld smartphones and non-static mounted cameras. The proposed license plate recognition pipeline filters to sharp frames, then sends a multimodal prompt to a VLM using several prompt strategies. Make and model recognition pipeline runs the same VLM with a revised prompt and an optional self-reflection module. In the self-reflection module, the model contrasts the query image with a reference from a 134-class dataset, correcting mismatches. Experiments on a smartphone dataset collected on the campus of the University of Texas at Austin, achieve top-1 accuracies of 91.67% for ALPR and 66.67% for make and model recognition. On the public UFPR-ALPR dataset, the approach attains 83.05% and 61.07%, respectively. The self-reflection module further improves results by 5.72% on average for make and model recognition. These findings demonstrate that VLMs provide a cost-effective solution for scalable, in-motion traffic video analysis.