We investigate the violation of the first Hund's rule in $4d$ and $5d$ transition-metal oxides that form solids of dimers. Bonding states within these dimers reduce the magnetization of such materials. We parametrize the dimer formation with realistic hopping parameters and find not only regimes where the system behaves like a Fermi liquid or as a Peierls insulator, but also strongly correlated regions due to Hund's coupling and its competition with the dimer formation. The electronic structure is investigated using the cluster dynamical mean-field theory for a dimer in the two-plane Bethe lattice with two orbitals per site and $3/8$ filling, which is three electrons per dimer. It reveals dimer-antiferromagnetic order of a high-spin (double-exchange) state and a low-spin (molecular-orbital) state. At the crossover region, we observe the suppression of long-range magnetic order, fluctuation enhancement, and renormalization of electron masses. At certain interaction strengths, the system becomes an incoherent antiferromagnetic metal with well-defined local moments.