When assisting people in daily tasks, robots need to accurately interpret visual cues and respond effectively in diverse safety-critical situations, such as sharp objects on the floor. In this context, we present M-CoDAL, a multimodal-dialogue system specifically designed for embodied agents to better understand and communicate in safety-critical situations. The system leverages discourse coherence relations to enhance its contextual understanding and communication abilities. To train this system, we introduce a novel clustering-based active learning mechanism that utilizes an external Large Language Model (LLM) to identify informative instances. Our approach is evaluated using a newly created multimodal dataset comprising 1K safety violations extracted from 2K Reddit images. These violations are annotated using a Large Multimodal Model (LMM) and verified by human annotators. Results with this dataset demonstrate that our approach improves resolution of safety situations, user sentiment, as well as safety of the conversation. Next, we deploy our dialogue system on a Hello Robot Stretch robot and conduct a within-subject user study with real-world participants. In the study, participants role-play two safety scenarios with different levels of severity with the robot and receive interventions from our model and a baseline system powered by OpenAI's ChatGPT. The study results corroborate and extend the findings from the automated evaluation, showing that our proposed system is more persuasive in a real-world embodied agent setting.