Our approach for the derivation of the exact (non-relativistic) translational-rovibronic Hamiltonian, based on the Hamiltonian operator in tensor form, is now extended to cases in which a body-fixed frame is defined via the introduction of two Euler angles (two-rotationalangle embedding). Diatomic molecules and diatom-diatom systems are considered as examples for this general formulation. For comparison, the three-rotational-angle embedding version of the diatom-diatom Hamiltonian is also derived.