Here's something I always remember to forget to do in cases like this - duplicate the static structural system, convert it to a modal one, and solve for a few natural frequencies. Look for zero or near-zero natural frequencies and associated rigid body modes. This can be used to identify the motion that your presumably inadequate constraints allow and shine a light on what needs to be done to fix them. Also, please look closely at your mesh. From the forgoing discussion and images (thanks for these!) I frankly cannot see how this would be possible, but your model almost acts as if it isn't joined by nodal connectivity - like there is a dissimilar mesh at an interface and no bonded contact to structurally connect the meshes at the interface.