We propose Destin2, a novel statistical and computational method for cross-modality dimension reduction, clustering, and trajectory reconstruction for single-cell ATAC-seq data. The framework integrates cellular-level epigenomic profiles from peak accessibility, motif deviation score, and pseudo-gene activity and learns a shared manifold using the multimodal input, followed by clustering and/or trajectory inference. We apply Destin2 to real scATAC-seq datasets with both discretized cell types and transient cell states and carry out benchmarking studies against existing methods based on unimodal analyses. Using cell-type labels transferred with high confidence from unmatched single-cell RNA sequencing data, we adopt four performance assessment metrics and demonstrate how Destin2 corroborates and improves upon existing methods. Using single-cell RNA and ATAC multiomic data, we further exemplify how Destin's cross-modality integrative analyses preserve true cell-cell similarities using the matched cell pairs as ground truths. Destin2 is compiled as a freely available R package available at https://github.com/yuchaojiang/Destin2.