This paper proposes a robust video streaming scheme for priority networks with path diversity, based on a combined approach of multiple description coding (MDC) with optimal picture classification into two priorities. A binary classification algorithm is proposed to define high (HP) and low (LP) priority network abstraction layer units (NALU), which in turn define the packet priorities. An optimisation algorithm is used to find HP pictures, based on dynamic programming and relying on minimisation of the packet loss concealment distortion. The paper shows that the proposed algorithm is able to effectively improve the decoded video without increasing the MDC stream redundancy. The overall performance evaluation, carried out by simulating MDC video streaming over lossy networks with path diversity, demonstrates that the proposed algorithm yields higher video quality for a wide range of packet loss rates (PLR). Comparing with no-priority MDC video streaming schemes, the simulation results show that the proposed algorithm can improve the average PSNR results in 0.7-3.2dB for packet loss rates between 3% and 15%.