You can show/hide a specific widget from the desktop on mobile using the in-built Customizer.
Apart from that, you can also change the ordering of the widgets using drag-n-drop functionality.
Follow the steps below:
Step 1: Click on the 'Edit' button to open the Customizer
Step 2: Click on the Widget Visibility option
Step 3: Click on the eye icon of a widget to control its visibility
Step 4: Drag-and-drop the widgets to re-arrange their position
You can also re-arrange the widgets specifically for mobile from here: