This paper reports the temperature dependence of the relaxation time T1 (55.2 and 90 MHz) and the second moment of the NMR line for protons in a polycrystalline sample of [NH2(CH3)2]3Sb2Cl9 (DMACA). The fundamental aspects of molecular dynamics from quantum tunneling at low temperatures to thermally activated reorientation at elevated temperatures have been studied. The experimentally observed spin-lattice relaxation rate is a consequence of dipolar interactions between the spin pairs inside the methyl group (1/T(1AE) contribution) as well as the spins belonging to neighboring methyl groups and pairs, methyl spin-outer methyl spin (1/T(1EE) contribution). These contributions are considered separately. Two methyl groups in the dimethylammonium (DMA) cations are dynamically inequivalent. The values of the tunnel splitting of separate methyl groups are obtained from the T1 (55.2 MHz) experiment. The tunneling dynamics taking place below the characteristic temperatures 74 and 42 K for separate methyl groups are discussed in terms of the Schrödinger equation. These temperatures point to the one at which thermal energy C(p)T and potential barrier take the same value. It is established that the second moment of the proton NMR line below 74 K up to liquid helium temperature is much lower than the rigid lattice value, which is due to a tunneling stochastic process of the methyl groups.