When a radio button has the focus but is not selected, I expect the space bar (on Windows at least) to select the button. This doesn't work, as you can verify with this small test program:

import javafx.application.Application;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.control.RadioButton;
import javafx.scene.control.ToggleGroup;
import javafx.scene.layout.BorderPane;
import javafx.scene.layout.FlowPane;
import javafx.stage.Stage;

public class RadioButtonTest extends Application {

    @Override
    public void start(Stage stage) {
        stage.setTitle("Radio Button Test");
        RadioButton button1 = new RadioButton("Option 1");
        RadioButton button2 = new RadioButton("Option 2");
        RadioButton button3 = new RadioButton("Option 3");
        FlowPane flow = new FlowPane();
        flow.getChildren().add(button1);
        flow.getChildren().add(button2);
        flow.getChildren().add(button3);
        ToggleGroup group = new ToggleGroup();
        group.getToggles().add(button1);
        group.getToggles().add(button2);
        group.getToggles().add(button3);
        BorderPane pane = new BorderPane();
        pane.setTop(new Button("Button"));
        pane.setCenter(flow);
        pane.setBottom(new Button("Another button"));
        stage.setScene(new Scene(pane));
        stage.setWidth(400);
        stage.setHeight(300);
        stage.show();
    }

    public static void main(String[] args) {
        launch(args);
    }

}