This paper presents the first findings on the molecular dynamics of the remarkable new class of linear and precisely functionalized ethylene copolymers. Specifically, we utilize broadband dielectric relaxation spectroscopy to investigate the molecular dynamics of linear polyethylene (PE)-based ionomers containing 1-methylimidazolium bromide (ImBr) pendants on exactly every 9th, 15th, or 21st carbon atom, along with one pseudorandom analogue. We also employed FTIR spectroscopy to provide insight into local ionic interactions and the nature of the ordering of the ethylene spacers between pendants. Prior X-ray scattering experiments revealed that the polar ionic groups in these ionomers self-assemble into microphase-separated aggregates dispersed throughout the nonpolar PE matrix. We focus primarily on the dynamics of the segmental relaxations, which are significantly slowed down compared to linear PE due to ion aggregation. Relaxation times depend on composition, the presence of crystallinity, and microphase-separated morphologies. Segmental relaxation strengths are much lower than predicted by the Onsager theory for mobile isolated dipoles but much higher than linear PE, demonstrating that at least some ImBr pendants participate in the segmental process. Analysis of the relaxation strengths using the Kirkwood g correlation factor demonstrates that ca. 10-40% of the ImBr ion dipoles (depending on copolymer composition and temperature) participate in the segmental motions of the precise ionomers under study, with the remainder immobilized or having net antiparallel arrangements in ion aggregates.