After you rescue Paula, you can try to reach the next Your Sanctuary location east of Happy-Happy Village, or you can come back later.
Raise Paula to level 8 before you try to go through this cave.
Go to Mondo Mole
Go into the cave east of Happy-Happy Village. If you want Paula to gain some levels first, have Ness use Paralysis on the Moles Playing Rough, then when you are done raising Paula's levels, leave the cave and rest up before you try to go to the cave boss.
At first, the path is straightforward, but then it splits into a southern path and an eastern path. Go south first to get a Great Charm. The Great Charm protects against Paralysis, and also increases speed. Equip the Great Charm on Ness, and equip the Travel Charm on Paula.
Go back to where the path split. Go east, and keep going east if you want a Croissant. Then go west until you can go south. After you go south, the path is straightforward for a while. You will find an area that has a Magic Butterfly.
After you go up a slope and go north, you will reach a pool of water. Go east on the path south of the water. Then get the PSI Caramel near the east side of the water.
Go east from there to reach Mondo Mole.
Start by casting Paralysis. It almost always works against Mondo Mole. The mole is weak to Fire. If the mole uses a psychic shield, use physical attacks until the shield goes away. If you are having trouble keeping Paula alive, just let her die and have Ness focus on killing the mole.
Get the Melody
After you defeat Mondo Mole, go through the door and approach the tiny footsteps to get the Sound Stone melody.