Recently, dual-target cross-domain recommendation (DTCDR) has been proposed to alleviate the data sparsity problem by sharing the common knowledge across domains simultaneously. However, existing methods often assume that personal data containing abundant identifiable information can be directly accessed, which results in a controversial privacy leakage problem of DTCDR. To this end, we introduce the P2DTR framework, a novel approach in DTCDR while protecting private user information. Specifically, we first design a novel inter-client knowledge extraction mechanism, which exploits the private set intersection algorithm and prototype-based federated learning to enable collaboratively modeling among multiple users and a server. Furthermore, to improve the recommendation performance based on the extracted common knowledge across domains, we proposed an intra-client enhanced recommendation, consisting of a constrained dominant set (CDS) propagation mechanism and dual-recommendation module. Extensive experiments on real-world datasets validate that our proposed P2DTR framework achieves superior utility under a privacy-preserving guarantee on both domains.