The nested panel only needs 3 parameters; Height, Width and Thickness. IT DOES NOT NEED ANGLE PARAMETERS -- or Ref. Lines. The Angle of the Panel is driven by the Ref. Line it is hosted to in the Parent Family. Just create those 3 parameters (and maybe one for Materials too) and then under the Properties, check the box next to "Work Plane-Based" -- then load the Panel into Parent Family (e.g. the one with the Ref. Lines). Before you place an Instance of the Panel in the Parent Family, set one of the two Ref. Planes as the "Current" Work Plane and then place a Panel ON TOP OF THAT REF. LINE WORK PLANE. After it's placed, Align/Lock the Panel to the Ref. Line. Repeat for second panel, choosing the OTHER Ref. Line as the Work Plane Host. Now, when the Ref. Lines move/rotate, the Panels move/rotate with their respective Ref. Lines. You don't need to do anything else to the Panels except associate their Height, Width, Thickness and Material Parameters to Parent Family Parameters.
Now, I notice the Family I sent you is not using nested Families for the Panels. I would suggest nesting the Panels, but you could do what I did in my Family and sketch extrusions on top of each Ref. Line. Best way to do this, is to make a Ref. Line the "CURRENT" Work Plane and then create the Panel/extrusion.
...one more important direction: if you do draw extrusions for Panel, instead of nesting them, make darn sure that labeled dimensions for Height, Width and Thickness are ONLY pulled from the hosting Ref. Line, or between extrusion sketch linework or extrusion edges. Don't reference anything beyond the Ref. Line Work Plane that the extrusions are drawn on.