The TabPane, if setting a prefWidth without setting minWidth, will use prefWidth as minWidth. The result is the dividers cannot be dragged when they are added to a SplitPane.

import javafx.application.Application;
import javafx.geometry.Orientation;
import javafx.scene.Scene;
import javafx.scene.control.SplitPane;
import javafx.scene.control.Tab;
import javafx.scene.control.TabPane;
import javafx.scene.layout.BorderPane;
import javafx.scene.layout.Pane;
import javafx.scene.text.Text;
import javafx.stage.Stage;

public class SplitPaneDemo extends Application {
    public static void main(String[] args) {
        launch(args);
    }

    @Override
    public void start(Stage stage) {
        // create some tabs.
        final TabPane tabPane1 = createTabPane(200, 100);
        final TabPane tabPane2 = createTabPane(200, 20);
        final TabPane tabPane3 = createTabPane(200, 20);

        SplitPane splitPane = new SplitPane();
        splitPane.setOrientation(Orientation.HORIZONTAL);
        splitPane.getItems().addAll(tabPane1, tabPane2, tabPane3);
        Scene scene = new Scene(splitPane);
        splitPane.prefHeightProperty().bind(scene.heightProperty());
        splitPane.prefWidthProperty().bind(scene.widthProperty());
        stage.setScene(scene);
        stage.show();
    }

    private TabPane createTabPane(double pref, double min) {
        final TabPane tabPane = new TabPane();
        Tab tab1 = new Tab("Sites");
        tab1.setContent(createPane("lightgreen"));
        Tab tab2 = new Tab("Favorites");
        tab2.setContent(createPane("lightsteelblue"));
        Tab tab3 = new Tab("Loves");
        tab3.setContent(createPane("pink"));
        tabPane.getTabs().addAll(tab1, tab2, tab3);
        tabPane.setPrefSize(pref, 200);
// tabPane.setMinSize(min, 200);
        return tabPane;
    }

    // create a pane of a given color to hold tab content.
    private Pane createPane(String color) {
        final BorderPane pane = new BorderPane();
        Text text = new Text();
        text.textProperty().bind(pane.widthProperty().asString().concat(" x ").concat(pane.heightProperty().asString()));
        pane.setCenter(text);
        return pane;
    }
}

A possible workaround is to specify the minWidth as well. However, if setResizableWithParent is used, the initial size of the panes will be the minWidth, not the prefWidth. Here is a modified test case from above to demo this issue. Note that the width of the second and third TabPane is 20, not 200.

package jidefx.playground;

import javafx.application.Application;
import javafx.geometry.Orientation;
import javafx.scene.Scene;
import javafx.scene.control.SplitPane;
import javafx.scene.control.Tab;
import javafx.scene.control.TabPane;
import javafx.scene.layout.BorderPane;
import javafx.scene.layout.Pane;
import javafx.scene.text.Text;
import javafx.stage.Stage;

public class SplitPaneDemo extends Application {
    public static void main(String[] args) {
        launch(args);
    }

    @Override
    public void start(Stage stage) {
        // create some tabs.
        final TabPane tabPane1 = createTabPane(200, 100);
        final TabPane tabPane2 = createTabPane(200, 20);
        final TabPane tabPane3 = createTabPane(200, 20);

        SplitPane splitPane = new SplitPane();
        splitPane.setOrientation(Orientation.HORIZONTAL);
        splitPane.getItems().addAll(tabPane1, tabPane2, tabPane3);
        SplitPane.setResizableWithParent(tabPane1, true);
        SplitPane.setResizableWithParent(tabPane2, false);
        SplitPane.setResizableWithParent(tabPane3, false);
        Scene scene = new Scene(splitPane);
        splitPane.prefHeightProperty().bind(scene.heightProperty());
        splitPane.prefWidthProperty().bind(scene.widthProperty());
        stage.setScene(scene);
        stage.show();
    }

    private TabPane createTabPane(double pref, double min) {
        final TabPane tabPane = new TabPane();
        Tab tab1 = new Tab("Sites");
        tab1.setContent(createPane("lightgreen"));
        Tab tab2 = new Tab("Favorites");
        tab2.setContent(createPane("lightsteelblue"));
        Tab tab3 = new Tab("Loves");
        tab3.setContent(createPane("pink"));
        tabPane.getTabs().addAll(tab1, tab2, tab3);
        tabPane.setPrefSize(pref, 200);
        tabPane.setMinSize(min, 200);
        return tabPane;
    }

    // create a pane of a given color to hold tab content.
    private Pane createPane(String color) {
        final BorderPane pane = new BorderPane();
        Text text = new Text();
        text.textProperty().bind(pane.widthProperty().asString().concat(" x ").concat(pane.heightProperty().asString()));
        pane.setCenter(text);
        pane.setStyle("-fx-background-color: " + color);
        return pane;
    }
}