Cation engineering provides a route to control the structure and properties of hybrid halide perovskites, which has resulted in the highest performance solar cells based on mixtures of Cs, methylammonium, and formamidinium. Here, we present a multi-technique experimental and theoretical study of structural phase transitions, structural phases and dipolar dynamics in the mixed methylammonium/dimethylammonium MA1-xDMAxPbBr3 hybrid perovskites (0 ≤ x ≤ 1). Our results demonstrate a significant suppression of the structural phase transitions, enhanced disorder and stabilization of the cubic phase even for a small amount of dimethylammonium cations. As the dimethylammonium concentration approaches the solubility limit in MAPbBr3, we observe the disappearance of the structural phase transitions and indications of a glassy dipolar phase. We also reveal a significant tunability of the dielectric permittivity upon mixing of the molecular cations that arises from frustrated electric dipoles.