Being able to accurately monitor the screen exposure of young children is important for research on phenomena linked to screen use such as childhood obesity, physical activity, and social interaction. Most existing studies rely upon self-report or manual measures from bulky wearable sensors, thus lacking efficiency and accuracy in capturing quantitative screen exposure data. In this work, we developed a novel sensor informatics framework that utilizes egocentric images from a wearable sensor, termed the screen time tracker (STT), and a vision language model (VLM). In particular, we devised a multi-view VLM that takes multiple views from egocentric image sequences and interprets screen exposure dynamically. We validated our approach by using a dataset of children's free-living activities, demonstrating significant improvement over existing methods in plain vision language models and object detection models. Results supported the promise of this monitoring approach, which could optimize behavioral research on screen exposure in children's naturalistic settings.