Recent advances in image understanding have enabled methods that leverage large language models for multimodal reasoning in remote sensing. However, existing approaches still struggle to steer models to the user-relevant regions when only simple, generic text prompts are available. Moreover, in large-scale aerial imagery many objects exhibit highly similar visual appearances and carry rich inter-object relationships, which further complicates accurate recognition. To address these challenges, we propose Cross-modal Context-aware Learning for Visual Prompt-Guided Multimodal Image Understanding (CLV-Net). CLV-Net lets users supply a simple visual cue, a bounding box, to indicate a region of interest, and uses that cue to guide the model to generate correlated segmentation masks and captions that faithfully reflect user intent. Central to our design is a Context-Aware Mask Decoder that models and integrates inter-object relationships to strengthen target representations and improve mask quality. In addition, we introduce a Semantic and Relationship Alignment module: a Cross-modal Semantic Consistency Loss enhances fine-grained discrimination among visually similar targets, while a Relationship Consistency Loss enforces alignment between textual relations and visual interactions. Comprehensive experiments on two benchmark datasets show that CLV-Net outperforms existing methods and establishes new state-of-the-art results. The model effectively captures user intent and produces precise, intention-aligned multimodal outputs.