To quickly use the mug with the barrel, start by selecting the note (pressing the down arrow key after opening your inventory) while walking to the scumm bar. Then, pick up the mugs, walk to the curtain and, while you wait for the screen to scroll, open the inventory, press the right arrow key so a mug gets the yellow box, and close the inventory before continuing to walk to the right. This way the mug will be ready to use when you enter the kitchen.