This paper deals with the problem of jointly designing the source precoder, the relaying matrices, and the destination equalizer in a multiple-relay amplify-and-forward (AF) cooperative multiple-input multiple-output (MIMO) wireless network, when partial channel-state information (CSI) is available. Specifically, the considered approaches are based on the knowledge of instantaneous CSI of the first-hop channel matrix, whereas only statistical CSI of the second-hop channels is assumed. In such a scenario, with respect to the case when instantaneous CSI of both the first- and second-hop MIMO channel matrices is exploited, existing network designs exhibit a significant performance degradation. Relying on a relaxed minimum-mean-square-error (MMSE) criterion, we show that the design based on the potential activation of all possible antennas for all available AF relays leads to a mathematically intractable optimization problem. Therefore, we develop a joint relay-and-antenna selection procedure that determines the best subset of the available antennas possibly belonging to different relays. Monte Carlo simulations show that, compared to designs based on the selection of the best relay, the proposed strategy offers a significant performance gain, by also outperforming other recently proposed relay/antenna selection schemes.