We investigated the antiferromagnetic phase transition in the frustrated and multiferroic hexagonal manganites h-YMnO₃ (YMO) and h-(Y_0.98Eu_0.02)MnO₃ (YEMO). Elastic neutron scattering was used to study, in detail, the phase transition in YMO and YEMO under zero pressure and in YMO under a hydrostatic pressure of 1.5 GPa. Under conditions of zero pressure, we found critical temperatures of T_N = 71.3(1) K and 72.11(5) K and the critical exponent 0.22(2) and β = 0.206(3), for YMO and YEMO, respectively. This is in agreement with earlier work by Roessli et al. Under an applied hydrostatic pressure of 1.5 GPa, the ordering temperature increased to T_N = 75.2(5) K, in agreement with earlier reports, while β was unchanged. Inelastic neutron scattering was used to determine the size of the anisotropy spin wave gap close to the phase transition. From spin wave theory, the gap is expected to close with a critical exponent, β', identical to the order parameter β. Our results indicate that the gap in YEMO indeed closes at T_N = 72.4(3) K with β' = 0.24(2), while the in-pressure gap in YMO closes at 75.2(5) K with an exponent of β' = 0.19(3). In addition, the low temperature anisotropy gap was found to have a slightly higher absolute value under pressure. The consistent values obtained for β in the two systems support the likelihood of a new universality class for triangular, frustrated antiferromagnets.