In this paper, we examine orthogonal space-time block coding with receiver maximal ratio combining (OSTBC/MRC) and selection combining (OSTBC/SC) in multiple-input-multiple-output (MIMO) decode-and-forward (DF) relay networks with underlay spectrum sharing, considering optimal and suboptimal cases. The secondary network under consideration is equipped with multiple correlated antennas at the source, the relay, and the destination. On the other hand, the primary network is composed of L primary users (PUs), each of which is equipped with multiple correlated antennas. For the considered underlay spectrum sharing, the transmit power condition is related by an interference limit on the primary network and the maximum transmission power in the secondary network. In particular, new exact expressions for the outage probability of the adopted system models are obtained. Moreover, simple asymptotic expressions for the outage probability are provided to enable the characterization of the achievable diversity orders and coding gains. To enhance the secondary network performance, optimal power allocation (PA) between the secondary source and the secondary relay is obtained based on the asymptotic outage probability under the constraints of total allowable transmit power at the secondary user (SU) and maximum allowable interference power limit at the PU. The derived analytical formulas herein are supported by numerical results to clarify the main contributions.