Deformable objects manipulation can benefit from representations that seamlessly integrate vision and touch while handling occlusions. In this work, we present a novel approach for, and real-world demonstration of, multimodal visuotactile state-estimation and dynamics prediction for deformable objects. Our approach, VIRDO++, builds on recent progress in multimodal neural implicit representations for deformable object state-estimation (link) via a new formulation for deformation dynamics and a complementary state-estimation algorithm that (i) maintains a belief distribution of deformation within a trajectory, and (ii) enables practical real-world application by removing the need for contact patches. In the context of two real-world robotic tasks, we show: (i) high-fidelity cross-modal state-estimation and prediction of deformable objects from partial visuo-tactile feedback, and (ii) generalization to unseen objects and contact formations.