This paper jointly designs power allocation and two-dimensional (2-D) equalizers for multiple relay nodes in a distributed multiple-input multiple-output (MIMO) relay network. Based on the minimum mean-square error (MMSE) criterion, 2-D temporal-and-spatial equalizers are investigated at relays with a total equalizer power constraint for equalizing-and-forwarding the signals from the source to the destination in multipath fading channels, which has not been addressed in the existing literature. A bisection algorithm is proposed to obtain the optimal solution by utilizing the Karush-Kuhn-Tucker (K.K.T.) conditions. With the proposed 2-D equalizers, the distributed MIMO relay network can not only effectively mitigate the inter-symbol interference (ISI) and multiple-antenna interference (MAI) but also achieve the spatial and multipath diversity gains. Simulation results show that the proposed scheme can provide a substantial performance gain in terms of the bit error rate (BER) as compared with the conventional one-tap equalizer scheme for distributed MIMO relay systems.