Do these two disks have optical surfaces? I assume that is why you want to track the tip/tilt of them. Are these optically flat mirrors or windows or does the surface have some curvature?
Optical parts are fastened to a barrel or some other mechanical part to support them. It is troubling to have rigid body motion in the xz plane because you haven't added sufficient constraints to support the optical parts. I suggest you do that before you try to measure tip/tilt.
Mechanical parts are supported on an optical bench, which you consider to be ground in this simulation. It is unusual to have four support areas on the mechanical part becuase that leads to problems when the four legs have any kind of variation or have different themal expansions when the temperature change is different on one leg than another. Three supports is a typical design for connecting the mechanical part to the optical bench.
Whether you have 3 or 4 supports, it is always best to have that support be a finite area. Whenever solid elements are used, avoid supporting individual nodes because that creates a theoretically infinite stress due to a node having zero area.