Example of a problem with nesting objects in a groups and using bindings.

DragTest.java

package javafxapplication1;

import javafx.application.Application;
import javafx.event.EventHandler;
import javafx.scene.Group;
import javafx.scene.Node;
import javafx.scene.Scene;
import javafx.scene.input.MouseEvent;
import javafx.scene.paint.Color;
import javafx.scene.shape.Circle;
import javafx.scene.shape.CircleBuilder;
import javafx.scene.shape.Line;
import javafx.scene.shape.LineBuilder;
import javafx.scene.shape.Rectangle;
import javafx.scene.shape.RectangleBuilder;
import javafx.stage.Stage;

public class DragTest extends Application{
	final MoveContext moveContext = new MoveContext();
	
	
	@Override
	public void start(Stage stage) throws Exception {
		Group root = new Group();
		
		Circle c1 = createCircle();
		c1.setCenterX(100);
		c1.setCenterY(100);
		c1.setOnMousePressed(circleMoveEventHandler);
		c1.setOnMouseDragged(circleMoveEventHandler);
		
		
		Circle c2 = createCircle();
		c2.setCenterX(100);
		c2.setCenterY(500);
		c2.setOnMousePressed(circleMoveEventHandler);
		c2.setOnMouseDragged(circleMoveEventHandler);
		
		Circle c3 = createCircle();
		c3.setCenterX(500);
		c3.setCenterY(100);
		c3.setOnMousePressed(circleMoveEventHandler);
		c3.setOnMouseDragged(circleMoveEventHandler);
		
		Circle c4 = createCircle();
		c4.setCenterX(500);
		c4.setCenterY(500);
		c4.setOnMousePressed(circleMoveEventHandler);
		c4.setOnMouseDragged(circleMoveEventHandler);
		
		Line c1c2 = createLine();
		c1c2.startXProperty().bind(c1.centerXProperty());
		c1c2.startYProperty().bind(c1.centerYProperty());
		c1c2.endXProperty().bind(c2.centerXProperty());
		c1c2.endYProperty().bind(c2.centerYProperty());
		
		Line c3c4 = createLine();
		c3c4.startXProperty().bind(c3.centerXProperty());
		c3c4.startYProperty().bind(c3.centerYProperty());
		c3c4.endXProperty().bind(c4.centerXProperty());
		c3c4.endYProperty().bind(c4.centerYProperty());
		
		Line c1c4 = createLine();
		c1c4.startXProperty().bind(c1.centerXProperty());
		c1c4.startYProperty().bind(c1.centerYProperty());
		c1c4.endXProperty().bind(c4.centerXProperty());
		c1c4.endYProperty().bind(c4.centerYProperty());
		
		Group moveableGroup = new Group();
		Rectangle r = RectangleBuilder.create()
				.x(450)
				.y(50)
				.width(100)
				.height(500)
				.fill(Color.LIGHTGRAY)
				.build();
		moveableGroup.getChildren().addAll(r, c3, c4, c3c4);
		moveableGroup.setOnMousePressed(groupMoveEventHandler);
		moveableGroup.setOnMouseDragged(groupMoveEventHandler);
		
		root.getChildren().addAll(c1, c2,  c1c2, c1c4, moveableGroup);
		Scene scene = new Scene(root, 600, 600);
		stage.setScene(scene);
		stage.setTitle("Drag Test");
		stage.show();
	}
	
	public Circle createCircle(){
		return CircleBuilder.create()
				.radius(25)
				.fill(Color.AQUAMARINE)
				.build();
	}
	
	public Line createLine(){
		return LineBuilder.create()
				.stroke(Color.BLACK)
				.strokeWidth(2)
				.build();
	}
	
	public static void main(String[] args) {
		launch(args);

	}
	
	EventHandler<MouseEvent> circleMoveEventHandler =  new EventHandler<MouseEvent>(){
		@Override
		public void handle(MouseEvent event) {
			if(event.getEventType().equals(MouseEvent.MOUSE_PRESSED)){
				Circle node = (Circle) event.getSource();
				
				moveContext.setMouseAnchorX(event.getX());
				moveContext.setMouseAnchorY(event.getY());
				moveContext.setInitialTranslateX(node.getCenterX());
				moveContext.setInitialTranslateY(node.getCenterY());
				event.consume();
			}else if(event.getEventType().equals(MouseEvent.MOUSE_DRAGGED)){
				Circle node = (Circle) event.getSource();
				
				node.setCenterX(moveContext.getDragDestX(event.getX()));
				node.setCenterY(moveContext.getDragDestY(event.getY()));
				event.consume();
				
			}
			
			
		}
	};
	
	EventHandler<MouseEvent> groupMoveEventHandler =  new EventHandler<MouseEvent>(){
		@Override
		public void handle(MouseEvent event) {
			if(event.getEventType().equals(MouseEvent.MOUSE_PRESSED)){
				Node node = (Node) event.getSource();
				
				moveContext.setMouseAnchorX(event.getX());
				moveContext.setMouseAnchorY(event.getY());
				moveContext.setInitialTranslateX(node.getLayoutX());
				moveContext.setInitialTranslateY(node.getLayoutY());
			}else if(event.getEventType().equals(MouseEvent.MOUSE_DRAGGED)){
				Node node = (Node) event.getSource();
				
				node.setLayoutX(moveContext.getDragDestX(event.getX()));
				node.setLayoutY(moveContext.getDragDestY(event.getY()));
				
			}
			
			
		}
	};
	
	class MoveContext {
		private double mouseAnchorX;
	    private double mouseAnchorY;
	    
	    private double initialTranslateX;
	    private double initialTranslateY;

	    public MoveContext(){
	    	this(0,0,0,0);
	    }

	    /**
	     * Create a move context
	     * @param mouseAnchorX - start mouse x position
	     * @param mouseAnchorY - start mouse y position
	     * @param initialTranslateX - initial object x position
	     * @param initialTranslateY - initial object y position
	     */
		public MoveContext(double mouseAnchorX, double mouseAnchorY,
				double initialTranslateX, double initialTranslateY) {
			this.mouseAnchorX = mouseAnchorX;
			this.mouseAnchorY = mouseAnchorY;
			this.initialTranslateX = initialTranslateX;
			this.initialTranslateY = initialTranslateY;
		}
	    
		public double getDragDestX(double destX){
	        return initialTranslateX + destX - mouseAnchorX;
	    }
	    
	    public double getDragDestY(double destY){
	        return initialTranslateY + destY - mouseAnchorY;
	    }

	    /**
	     * Get the value of initialTranslateY
	     *
	     * @return the value of initialTranslateY
	     */
	    public double getInitialTranslateY() {
	        return initialTranslateY;
	    }

	    /**
	     * Set the value of initialTranslateY
	     *
	     * @param initialTranslateY new value of initialTranslateY
	     */
	    public void setInitialTranslateY(double initialTranslateY) {
	        this.initialTranslateY = initialTranslateY;
	    }

	    /**
	     * Get the value of initialTranslateX
	     *
	     * @return the value of initialTranslateX
	     */
	    public double getInitialTranslateX() {
	        return initialTranslateX;
	    }

	    /**
	     * Set the value of initialTranslateX
	     *
	     * @param initialTranslateX new value of initialTranslateX
	     */
	    public void setInitialTranslateX(double initialTranslateX) {
	        this.initialTranslateX = initialTranslateX;
	    }

	    /**
	     * Get the value of mouseAnchorY
	     *
	     * @return the value of mouseAnchorY
	     */
	    public double getMouseAnchorY() {
	        return mouseAnchorY;
	    }

	    /**
	     * Set the value of mouseAnchorY
	     *
	     * @param mouseAnchorY new value of mouseAnchorY
	     */
	    public void setMouseAnchorY(double mouseAnchorY) {
	        this.mouseAnchorY = mouseAnchorY;
	    }


	    /**
	     * Get the value of mouseAnchorX
	     *
	     * @return the value of mouseAnchorX
	     */
	    public double getMouseAnchorX() {
	        return mouseAnchorX;
	    }

	    /**
	     * Set the value of mouseAnchorX
	     *
	     * @param mouseAnchorX new value of mouseAnchorX
	     */
	    public void setMouseAnchorX(double mouseAnchorX) {
	        this.mouseAnchorX = mouseAnchorX;
	    }

	    @Override
	    public String toString() {
	        return "MoveContext{" + "mouseAnchorX=" + mouseAnchorX + ", mouseAnchorY=" + mouseAnchorY + ", initialTranslateX=" + initialTranslateX + ", initialTranslateY=" + initialTranslateY + '}';
	    }
	    
	}

}