please define Ydirection (it might be the transverse direction towards the riding one) and describe if you need to know the whole chassis stiffness or only the bracket one.
It's quite easy for you if you can build a 3D model of your chassis. After that, some FEM software can help you to calculate the deformation of chassis with corresponding load. The stiffness of chasis can be obtained: Stiff=Load/Deform