Magnetic properties and underlying magnetic models of the synthetic A2Cu3O(SO4)3 fedotovite (A = K) and puninite (A = Na) minerals, as well as the mixed euchlorine-type NaKCu3O(SO4)3 are reported. We show that all three compounds contain magnetic Cu6 hexamer units which at temperatures below about 100 K act as single spin-1 entities. Weak interactions between these magnetic molecules lead to long-range order below TN=3.4K (A = Na), 4.7 K (A = NaK), and about 3.0 K (A = K). The formation of the magnetic order is elucidated by ab initio calculations that reveal two-dimensional interhexamer interactions within crystallographic bc planes. This model indicates the presence of a weakly distorted square lattice of S=1 magnetic ions and challenges the earlier description of the A2Cu3O(SO4)3 minerals in terms of Haldane spin chains.