From JavaFX Pane documentation:
This class may be used directly in cases where absolute positioning of children is required since it does not perform layout beyond resizing resizable children to their preferred sizes. It is the application's responsibility to position the children since the pane leaves the positions alone during layout.
So, you cannot reach your goal by using basic Panes as children. Better try to use StackPanes instead:
A stackpane's parent will resize the stackpane within the stackpane's resizable range during layout.
A stackpane's unbounded maximum width and height are an indication to the parent that it may be resized beyond its preferred size to fill whatever space is assigned to it.
Take a look at this example (I added background colors to the StackPanes, since I used SceneBuilder to test the behavior) and tell me please if it satisfies your needs:
<HBox maxHeight="1.7976931348623157E308" maxWidth="1.7976931348623157E308" prefHeight="1000.0" prefWidth="1236.0" style="-fx-background-color: lightblue;" xmlns="http://javafx.com/javafx/8.0.40" xmlns:fx="http://javafx.com/fxml/1">
<children>
<StackPane fx:id="leftPane" maxHeight="10000.0" maxWidth="120.0" minHeight="400.0" minWidth="100.0" prefHeight="10000.0" prefWidth="120.0" style="-fx-background-color: red;" />
<StackPane fx:id="centerPane" maxHeight="10000.0" maxWidth="10000.0" minHeight="400.0" minWidth="120.0" prefHeight="10000.0" style="-fx-background-color: white;">
<children>
<Label prefWidth="999.0" text="Label of example. Label of example. Label of example. Label of example. Label of example. Label of example. Label of example. Label of example. Label of example. Label of example. Label of example. " />
</children></StackPane>
<StackPane fx:id="rightPane" maxHeight="10000.0" maxWidth="120.0" minHeight="400.0" minWidth="100.0" prefHeight="10000.0" prefWidth="120.0" style="-fx-background-color: green;" />
</children></HBox>
You can also use other Pane or Box components instead.
Update:
The previous example makes the center Pane to dynamically adjust in function of the width of its children, fulfilling the parent Pane if needed, but never exceeding its maximum width. So, if you want the Pane to always fill the width of its parent, a big enough preferred width must be added to the center Pane.
<StackPane fx:id="centerPane" maxHeight="10000.0" minHeight="400.0" prefHeight="10000.0" prefWidth="1000.0"/>