As an emerging demand response (DR) resource, data centers (DCs) have garnered significant attention due to their ability to adapt to stochastic renewable energy fluctuations. To fully exploit the price signals from diverse markets and achieve the flexible complementarity between DCs and virtual power plant (VPP) resources, this paper proposes a coordinated framework for the data center virtual power plant (DCVPP) participating in the electricity -carbon joint market under uncertainty. Specifically, a refined model of power consumption for cooling system in DC is developed based on the second-order equivalent thermal parameter (ETP) theory, which enhances the accuracy of load modeling and maximizes the potential for DR. To address the penalty risks associated with forecast uncertainties in renewable energy generation and load demands, a risk-based reserve scheme is developed by integrating the Gaussian copula with two-sided superquantile theory. This scheme provides a coordinated mechanism for quantifying the correlations between forecast errors. On this basis, an optimal scheduling strategy of DCVPPs is formulated in the electricity-carbon joint market, which coordinates DC load flexibility with distributed energy resources to optimize economic performance and reduce carbon emissions. Case studies demonstrate that the proposed refined model achieves an root mean square error (RMSE) reduction ranging from 57.9% to 68.8%, and the risk-based reserve scheme reduces penalty costs by 24.4%. Furthermore, the integration of the carbon trading mechanism in the proposed optimal scheduling strategy results in an increase of $259.9 in economic benefits and an average reduction of 14% in carbon emissions.