We investigate the impact of Coulomb correlations on the low-energy collective excitations in two-dimensional electron systems in the quantum Hall state nu = 2. The collective excitations are studied using inelastic light scattering in the set of MgZnO/ZnO heterostructures with high-mobility two-dimensional electrons. The study focuses on the lowest-energy collective excitations in the paramagnetic state nu = 2, the cyclotron spin-flip magnetoexcitons (CSFMs), which are associated with inter-Landau-level transitions with a simultaneous spin flip. The Coulomb contribution to the CSFM energy is measured independently of the Zeeman term as a function of electron density. It is established that in the range of electron concentrations corresponding to the Wigner-Seitz parameter r(s) similar to 5-7, the combination of the Coulomb and Zeeman contributions leads to a softening of the CSFM. This softening accompanies spontaneous switching of the spin configuration in the nu = 2 quantum Hall system from paramagnetic to ferromagnetic. Theoretical estimates are given for the correlation energy terms of the CSFM responsible for its softening and a concomitant ferromagnetic transition.