This paper considers wireless multicast networks where network coding (NC) is applied to improve network throughput. A novel joint topology and cross-layer design is proposed to maximize the network throughput subject to various quality-of-service constraints, such as: wireless multicast rate, wireless link capacity, energy supply and network lifetime. Specifically, a heuristic NC-based link-controlled routing tree algorithm is developed to reduce the number of required intermediate nodes. The proposed algorithm facilitates the optimization of the wireless multicast rate, data flow of wireless links, energy supply and lifetime of nodes through a novel cross-layer design. The proposed joint topology and crosslayer design is evaluated and compared against other schemes from the literature. The results show that the proposed scheme can achieve up to 50% increase in the system throughput when compared to a classic approach.