Domain Generalization (DG) aims to train models that can effectively generalize to unseen domains. However, in the context of Federated Learning (FL), where clients collaboratively train a model without directly sharing their data, most existing DG algorithms are not directly applicable to the FL setting due to privacy constraints, as well as the limited data quantity and domain diversity at each client. To tackle these challenges, we propose FedCCRL, a lightweight federated domain generalization method that significantly improves the model's generalization ability while preserving privacy and ensuring computational and communication efficiency. Specifically, FedCCRL comprises two principal modules: the first is a cross-client feature extension module, which increases local domain diversity via cross-client domain transfer and domain-invariant feature perturbation; the second is a representation and prediction dual-stage alignment module, which enables the model to effectively capture domain-invariant features. Extensive experimental results demonstrate that FedCCRL achieves the state-of-the-art performance on the PACS, OfficeHome and miniDomainNet datasets across FL settings of varying numbers of clients. Code is available at https://github.com/sanphouwang/fedccrl