Build a new reference frame and generate rotation matrix between old and new reference frame

I have a 3D body with a cilinder on the side. Matlab automatically set the reference frame in the center of the object.

I want to change the reference frame, setting the new in the center of the cylinder, with the Z axis = cylinder axis and x and y direction between the center of my cylinder and 2 point on the body.

The cylinder center and direction, and the 2 points coordinates are known.