Recognizing speaker intent in long audio dialogues among speakers has a wide range of applications, but is a non-trivial AI task due to complex inter-dependencies in speaker utterances and scarce annotated data. To address these challenges, an end-to-end framework, namely DialogGraph-LLM, is proposed in the current work. DialogGraph-LLM combines a novel Multi-Relational Dialogue Attention Network (MR-DAN) architecture with multimodal foundation models (e.g., Qwen2.5-Omni-7B) for direct acoustic-to-intent inference. An adaptive semi-supervised learning strategy is designed using LLM with a confidence-aware pseudo-label generation mechanism based on dual-threshold filtering using both global and class confidences, and an entropy-based sample selection process that prioritizes high-information unlabeled instances. Extensive evaluations on the proprietary MarketCalls corpus and the publicly available MIntRec 2.0 benchmark demonstrate DialogGraph-LLM's superiority over strong audio and text-driven baselines. The framework demonstrates strong performance and efficiency in intent recognition in real world scenario audio dialogues, proving its practical value for audio-rich domains with limited supervision. Our code is available at https://github.com/david188888/DialogGraph-LLM.