Spatial multi-omics technologies enable joint profiling of molecular modalities within native tissue contexts, but integrating data across heterogeneous tissue sections and experimental batches remains a fundamental challenge. A key limitation of existing methods is that spatial graphs are constructed using manually defined radii or fixed neighbor sizes prior to training, preventing models from adapting spatial interaction scales across tissues with variable architectures and cell densities. To address this limitation, we propose SpaHMS, a fully dynamic framework for spatial multi-omics integration that learns hierarchical, multi-scale spatial receptive fields in an end-to-end manner. SpaHMS introduces a Dynamic Hierarchical Multi-Scale Graph Neural Network that jointly optimizes spatial graph structure and multimodal representations, enabling adaptive spatial modeling across heterogeneous tissues. Each modality is encoded using a dedicated network with cross-section parameter sharing, preserving modality-specific structure while mitigating batch effects through explicit mutual nearest neighbor (MNN) alignment. Across datasets involving RNA, ADT, and ATAC, SpaHMS produces robustly aligned, batch-corrected, and biologically coherent embeddings that preserve meaningful spatial organization.