Federated multi-view clustering (FedMVC) has been widely used to discover latent structures in distributed multi-view data, yet most methods still rely on the restrictive assumption of independent and identically distributed (IID) data. In practice, non-IID distributions with partial and imbalanced categories cause clients to learn biased and local representations, leading to model bias and unstable federated training performance. To address these issues, we propose a FedMVC framework called Bridging Inter-View and Client Heterogeneity: Federated Multi-View Clustering under Non-IID Data (H²-FedMVC), which tackles both inter-view and client heterogeneity in mixed-view settings. We propose a leader-guided learning mechanism to address inter-view heterogeneity by enhancing complementary and discriminative feature learning, and an expert adaptive aggregation strategy to handle client heterogeneity by prioritizing well-matched experts in global updates. Theoretical analysis and experiments demonstrate superior performance in heterogeneous mixed-view FedMVC settings, with code provided at https://github.com/JiazhenWang-0522/H2-FedMVC.