Recently, mobility support has become an important requirement in various Wireless Sensor Networks (WSNs). Low-power and Lossy Networks (LLNs) are a special type of WSNs that tolerate a certain degree of packet loss. However, due to the strict resource constraints in the computation, energy, and memory of LLNs, most routing protocols only support static network topologies. Data collection and data dissemination are two basic traffic modes in LLNs. Unlike data collection, data dissemination is less investigated in LLNs. There are two sorts of data-dissemination methods: point-to-multipoint and point-to-point. In this paper, we focus on the point-to-point method, which requires the source node to build routes to reach the destination node. We propose an adaptive routing protocol that integrates together point-to-point traffic and data-collection traffic, and supports highly mobile scenarios. This protocol quickly reacts to the movement of nodes to make faster decisions for the next-hop selection in data collection and dynamically build routes for point-to-point traffic. Results obtained through simulation show that our work outperforms two generic ad hoc routing protocols AODV and flooding on different performance metrics. Results also show the efficiency of our work in highly mobile scenarios with multiple traffic patterns.