This paper presents the design of an ad hoc two-way two-hop relay network using physical-layer network coding (PNC) in which multiple antennas are used at all nodes. In the considered network, the Alamouti's space-time block code (STBC) is used for transmission while linear detection is used for signal recovery. In order to facilitate linear estimation, we develop an equivalent multiuser STBC model for the proposed network and design the sum-and-difference matrix which allows convenient combination of the transmitted symbols from the end nodes. In addition, a simple relay selection method based on minimum mean square error (MSE) is proposed for performance improvement. Simulation results show that the proposed network achieves diversity order 2 while requiring only polynomial complexity. Moreover, it is possible to achieve significant bit error rate (BER) performance improvement when the proposed relay selection algorithm is used.