Under the "dual carbon" goals, an optimal scheduling method for the integrated energy system (IES) is proposed to promote its stable, low-carbon, and efficient operation, considering source-load uncertainty and green certificate-carbon trading. Firstly, to address the source-load uncertainty of the IES, the Latin hypercube sampling (LHS) method and the Kantorovich distance-based scenario reduction technique are adopted on the source side to characterize the output uncertainty of renewable energy. On the load side, an integrated demand response (IDR) model is established based on the coupling characteristics and response differences of various loads across multiple time scales. Secondly, the interaction mechanism between the green certificate market and the carbon trading market is analyzed. By converting held green certificates into carbon emission offsets via the Chinese certified emission reduction (CCER) mechanism, a novel framework for the green certificate-carbon collaborative trading mechanism is established. Finally, multiple time scales scheduling model for the IES is established, incorporating source-load uncertainty and the green certificate-carbon collaborative trading mechanism. Simulation results show that, under source-load uncertainty, the IES fully exploits multi-energy complementarity advantages, improving energy utilization efficiency by 10.03%. Guided by the green certificate-carbon collaborative trading mechanism, the total operating cost and carbon emissions of the IES are reduced by 3.35% and 11.99%, respectively.