The cooperative dynamics of a microlaser consisting of two threelevel atoms interacting with a pump field and two quantized cavity modes forming a radiative cascade are studied. Adiabatic elimination of one mode leads to a strong dynamical entanglement between the internal states of the atoms which allows us to study the effects of a cavity-mediated dipole-dipole interaction. We show that the coherent dynamics of the two-atom system will preferentially couple symmetrical linear combinations of internal states. If this coupling dominates the dynamics, the two-atom system will behave like a single atom with correspondingly larger dipole moment, that is a superradiant two-atom system. Even very small spontaneous decay causes transitions from symmetrical to antisymmetrical states and conversely. The hopping between two subsets of the state space can give rise to intriguing phenomena such as bistability of the laser mode intensity. By a randomization of the two coupling phases we recover the standard independent-atom laser theory.