This paper extends the distributed network utility maximization (NUM) framework to consider the case of resource sharing by multiple competing missions in a military-centric wireless sensor network (WSN) environment. Prior work on NUM-based optimization has considered unicast flows with sender-based utilities in either wireline or wireless networks. We extend the NUM framework to consider three key new features observed in mission-centric WSN environments: i) the definition of an individual mission's utility as a joint function of data from multiple sensor sources ii) the consumption of each senders (sensor) data by multiple receivers (missions) and iii) the multicast-tree based dissemination of each sensors data flow, using link-layer broadcasts to exploit the "wireless broadcast advantage" in data forwarding. We show how a receiver-centric, pricing-based, decentralized algorithm can ensure optimal and proportionally-fair rate allocation across the multiple missions, without requiring any coordination among independent missions (or sensors). We also discuss techniques to improve the speed of convergence of the protocol, which is essential in an environment as dynamic as the WSN.