Realistic reconstruction of two hands interacting with objects is a new and challenging problem that is essential for building personalized Virtual and Augmented Reality environments. Graph Convolutional networks (GCNs) allow for the preservation of the topologies of hands poses and shapes by modeling them as a graph. In this work, we propose the THOR-Net which combines the power of GCNs, Transformer, and self-supervision to realistically reconstruct two hands and an object from a single RGB image. Our network comprises two stages; namely the features extraction stage and the reconstruction stage. In the features extraction stage, a Keypoint RCNN is used to extract 2D poses, features maps, heatmaps, and bounding boxes from a monocular RGB image. Thereafter, this 2D information is modeled as two graphs and passed to the two branches of the reconstruction stage. The shape reconstruction branch estimates meshes of two hands and an object using our novel coarse-to-fine GraFormer shape network. The 3D poses of the hands and objects are reconstructed by the other branch using a GraFormer network. Finally, a self-supervised photometric loss is used to directly regress the realistic textured of each vertex in the hands' meshes. Our approach achieves State-of-the-art results in Hand shape estimation on the HO-3D dataset (10.0mm) exceeding ArtiBoost (10.8mm). It also surpasses other methods in hand pose estimation on the challenging two hands and object (H2O) dataset by 5mm on the left-hand pose and 1 mm on the right-hand pose.