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Orbital characteristics based on Gaia Early Data Release 3 astrometric parameters are analyzed for ${\sim} 1700$ $r$-process-enhanced (RPE; [Eu/Fe] $> +0.3$) metal-poor stars ([Fe/H] $\leq -0.8$) compiled from the $R$-Process Alliance, the GALactic Archaeology with HERMES (GALAH) DR3 survey, and additional literature sources. We find dynamical clusters of these stars based on their orbital energies and cylindrical actions using the \HDBSCAN ~unsupervised learning algorithm. We identify $36$ Chemo-Dynamically Tagged Groups (CDTGs) containing between $5$ and $22$ members; $17$ CDTGs have at least $10$ member stars. Previously known Milky Way (MW) substructures such as Gaia-Sausage-Enceladus, the Splashed Disk, the Metal-Weak Thick Disk, the Helmi Stream, LMS-1 (Wukong), and Thamnos are re-identified. Associations with MW globular clusters are determined for $7$ CDTGs; no recognized MW dwarf galaxy satellites were associated with any of our CDTGs. Previously identified dynamical groups are also associated with our CDTGs, adding structural determination information and possible new identifications. Carbon-Enhanced Metal-Poor RPE (CEMP-$r$) stars are identified among the targets; we assign these to morphological groups in the Yoon-Beers $A$(C)$_{c}$ vs. [Fe/H] Diagram. Our results confirm previous dynamical analyses that showed RPE stars in CDTGs share common chemical histories, influenced by their birth environments.