After Effect Expressions

If you want to animate Group 1/Transform Group 1/Rotation and automate the placement of the other objects (Rectangle 1 and 2), as long as all of the other properties are at their default settings, you can tie the Transform Rectangle 1/Anchor Point and the Transform Rectangle 1/Anchor point to the ellipse size with expressions, then tie Transform Rectangle 2/Position and Rotation to the Group 1/Transform Position and Rotation.

Here are the expressions:

//Transform Rectangle 1 Anchor Point
ElipseSize =  content("Group 1").content("Ellipse 1").content("Ellipse Path 1").size;
Rec1Size = content("Group 1").content("Rectangle 1").content("Rectangle Path 1").size/2;
[Rec1Size[0] - Rec1Size[1], Rec1Size[1]-ElipseSize[1]/2]

//Transform Rectangle 2 Anchor Point
refAP = content("Group 1").content("Rectangle 1").transform.anchorPoint;
[refAP[1], - refAP[0]]

// Transform Rectangle 2 Position
content("Group 1").transform.position

// Transform Rectangle 2 Rotation
content("Group 1").transform.rotation

If Rectangle 1 is not horizontal and Rectangle 2 is not vertical, you'll have to change both expressions or add an if statement to the expressions to figure out where to center the rotation.

I made the ellipse a vertical oval to make it easier to see it rotating. If your rotation center does not have equal sides, you will have to modify the expression to put the edge of the rotator against the edge of the rectangles or add another if/else statement. 

This is probably one of the simplest ways to link the layers with expressions instead of grouping them. Throw in 40 shapes that you want to link in various positions, and you can easily run into a very big mess in a very big hurry.

Here is what that looks like:

I have included an AE 23 project file with the post.