Go back and read basic woodworking texts because these are the sorts of things people have been solving for many years in a physics engine isn’t really going to speed up the process
I don't think this specific thing I am trying to solve is covered in a basic woodworking text. The table contains moving parts, and at this point I am trying to fix an existing design... But sure, I'll try that too! Thanks :)
Ah. I see- like a kinetic structure? I think Fusion 360 could probably help with this, but even better is blender. Blender contains 3D physics engine that can operate on models with constraints, so you'd basically just build a 3D working model of your moving parts table, and "simulate" it by moving parts along constrained paths. Then put a floor under it and measure the angles of the bases of the legs (assuming that's what's wobbly).
I was assuming you were just hitting the "it's hard to make a 4-legged table sit flat" or the "keeping attached legs attached firmly" problems.
Fusion 360 would add the ability to do FEM simulations, so in theory if you're torquing wood hard, you could see where the weakest point is, and add more material.
