The complex dynamics in supramolecular structures of poly(p-phenylenes) with short ethylene oxide (EO) side chains (known as "hairy rods") have been studied by combining temperature and pressure dependent dielectric spectroscopy (DS) with different nuclear magnetic resonance (NMR) techniques. The system forms a periodic lattice of layers of the main chains separated by layers of the amorphous EO chains. Since the dipole moment is located on the EO side chain, DS is probing mainly the side-chain motions and only indirectly the backbone dynamics. On the other hand, the different NMR techniques are also sensitive to the backbone mobility and provide the molecular origin of the dynamic processes. Two dielectrically active processes exist, a "fast" beta (which differs from the usual Johari-Goldstein beta process found in homopolymers and low molecular weight glass-forming liquids) and a "slow" alpha process with the latter carrying most of the intensity. Comparison of the NMR and dielectric results identifies the outer EO units as solely responsible for the dielectric beta process whereas both the short EO segments and the unfreezing of the internal backbone dynamics including bending motions contribute to the alpha process. The unfreezing of the backbone dynamics does not lead to the dissolution of the structure that only happens at even higher temperatures. Hairy rod molecules thus can serve as model systems which provide the means of studying the effect of confinement on the dynamics. In this respect, the effect of confinement is mainly on the temperature dependence of the alpha-process relaxation times.