Multi-modal object Re-identification refers to the task of identifying the same object from different cameras according to multi-modal cues. The existing multi-modal object Re-ID methods have achieved remarkable progress in extracting discriminative global and local representations. However, confined to learning generic static features, these approaches lack the relational structures and deep semantic reasoning needed for complex alignment, rendering them susceptible to modality noise as they passively aggregate information without filtering interference. To solve these problems, an LSR2 framework is imposed to actively mine relational and reasoning patterns. Specifically, the Representation Learning with Frequency Mining (RFM) module purifies features via frequency-domain decoupling. The Relational Expert System with Selective Reasoning (RER) then leverages expert guidance to adaptively filter relational cues. Finally, a Structural Consistency Constraint (SCC) enforces topological alignment to reduce high-dimensional mapping ambiguity. Extensive experiments on three object re-identification benchmark sets verify that by successfully learning rich relational and reasoning representations, the proposed method overcomes traditional modality noise and achieves superior performance.