Traffic measurement in high-speed network data streams plays a crucial role in many practical applications. Sketches have been widely used in approximate flow estimation due to their ability to maintain excellent accuracy and high throughput under limited memory resources. However, most existing sketch methods overlook the priority differences between flows. Although the number of high-priority flows is relatively lower, they contain essential information. Priority-aware sketch, a newly emerging category of sketches, aims to provide differentiated measurement accuracy for flows with different priorities. Unfortunately, these studies have focused solely on priority-aware per-flow size estimation tasks, and there is currently no related research on priority-aware per-flow spread estimation tasks. Priority-aware per-flow spread measurement holds significant potential in applications such as DDoS detection and Quality of Service enhancement for the data stream. To address this issue, we propose the P \(^2\) S-Sketch Family, consisting of three distinct sketches. They first estimate the spread of flows through the designed Estimator, then separate the flows according to their priorities, and finally store them in different structures. We conduct extensive experiments based on two real-world datasets, and the experimental results show that P \(^2\) S-Sketch Family outperforms prior works with 2.53 \(\times \) higher accuracy and 1.36 \(\times \) higher F1 score for high-priority flows.