Max-pressure (MP) control has proven effective at stabilizing network queues and improving traffic throughput in large-scale urban road networks. However, conventional connected-vehicle (CV)-based MP controllers face two critical limitations: in low-CV-penetration scenarios, their performance and practical stability may be compromised by sparse observations, and significant privacy concerns arise when utilizing individual vehicle data. To address these challenges, this paper proposes a novel data-fusion MP (DF-MP) controller that fuses data from both fixed-location detectors and CVs within a mobile edge computing architecture. To protect CV privacy, including macro-route information and micro-trajectory information, a privacy-preserving mechanism that combines homomorphic encryption, group signatures, hidden-matrix encoding, and a newly proposed adaptive randomized response strategy is further integrated with DF-MP to form Private-MP. Theoretical analysis shows that the proposed DF-MP and Private-MP controllers can stabilize network queues under the fusion framework, while the privacy-preserving mechanism of Private-MP limits disclosure to the movement-wise aggregate information required for control under the stated threat model. Simulation studies on a real-world network with 28 intersections show that Private-MP outperforms traditional detector-based MP control and remains more robust than CV-based MP at low penetration rates. At the same time, the performance loss caused by privacy protection remains small: compared with DF-MP, the increase in average vehicle delay of Private-MP is generally within 4%.