Cross-domain recommendation (CDR) aims to alleviate the data sparsity by transferring knowledge from an informative source domain to the target domain, which inevitably proposes stern challenges to data privacy and transferability during the transfer process. A small amount of recent CDR works have investigated privacy protection, while they still suffer from satisfying practical requirements (e.g., limited privacy-preserving ability) and preventing the potential risk of negative transfer. To address the above challenging problems, we propose a novel and unified privacy-preserving federated framework for dual-target CDR, namely P2FCDR. We design P2FCDR as peer-to-peer federated network architecture to ensure the local data storage and privacy protection of business partners. Specifically, for the special knowledge transfer process in CDR under federated settings, we initialize an optimizable orthogonal mapping matrix to learn the embedding transformation across domains and adopt the local differential privacy technique on the transformed embedding before exchanging across domains, which provides more reliable privacy protection. Furthermore, we exploit the similarity between in-domain and cross-domain embedding, and develop a gated selecting vector to refine the information fusion for more accurate dual transfer. Extensive experiments on three real-world datasets demonstrate that P2FCDR significantly outperforms the state-of-the-art methods and effectively protects data privacy.