Dialogue discourse parsing aims to identify and analyze discourse relations between the utterances within dialogues. However, linguistic features in dialogues, such as omission and idiom, frequently introduce ambiguities that obscure the intended discourse relations, posing significant challenges for parsers. To address this issue, we propose a Discourse-aware Clarification Module (DCM) to enhance the performance of the dialogue discourse parser. DCM employs two distinct reasoning processes: clarification type reasoning and discourse goal reasoning. The former analyzes linguistic features, while the latter distinguishes the intended relation from the ambiguous one. Furthermore, we introduce Contribution-aware Preference Optimization (CPO) to mitigate the risk of erroneous clarifications, thereby reducing cascading errors. CPO enables the parser to assess the contributions of the clarifications from DCM and provide feedback to optimize the DCM, enhancing its adaptability and alignment with the parser's requirements. Extensive experiments on the STAC and Molweni datasets demonstrate that our approach effectively resolves ambiguities and significantly outperforms the state-of-the-art (SOTA) baselines.