What happened to Rickon, Shaggy Dog and Osha and when did they split off from Bran, Hodor, Jojen and Meera as they went north of the Wall?
In A Dance with Dragons we learn that Rickon and Osha went to Skagos. Lord Manderly and Glover got that information from Wex, the mute Ironborn boy who was Theon's squire at Winterfell.
From the wiki:
Wex survived the sack of Winterfell carried out by Ramsay Snow by climbing the heart tree in the godswood. He witnesses the departure of Bran and Rickon Stark along with their direwolves and companions. He then proceeds to follow Rickon, Osha and Shaggydog to Skagos, before returning to civilization.
The Ironborn lad Wex Pyke followed them after they left Winterfell.
"The lad is ironborn, so he thought it best not to show himself," said Glover. "He listened. The six did not linger long amongst the ruins of Winterfell. Four went one way, two another. Wex stole after the two, a woman and a boy. He must have stayed downwind, so the wolf would not catch his scent."
"He knows where they went," Lord Wyman said.
"Where is the boy?" Somehow Davos knew he would not like the answer. "Where is it you want me to go, my lord?"
Robett Glover said, "Wex. Show him."
The mute flipped the dagger, caught it, then flung it end over end at the sheepskin map that adorned Lord Wyman's wall. It struck quivering. Then he grinned.
For half a heartbeat Davos considered asking Wyman Manderly to send him back to the Wolf's Den, to Ser Bartimus with his tales and Garth with his lethal ladies. In the Den even prisoners ate porridge in the morning. But there were other places in this world where men were known to break their fast on human flesh.
A Dance with Dragons, Davos IV
It is never made explicit in the text where Wex puts the knife into the map but it is almost certainly Skagos as cannibals live there.
Hardhome was once the only settlement approaching a town in the lands beyond the Wall, sheltered on Storrold's Point and commanding a deepwater harbor. But six hundred years ago, it was burned and its people destroyed, though the Watch cannot say for a certainty what happened. Some say that cannibals from Skagos fell on them, others that slavers from across the narrow sea were at fault. The strangest stories, from a ship of the Watch sent to investigate, tell of hideous screams echoing down from the cliffs above Hardhome, where no living man or woman could be found.
The World of Ice and Fire, The Wall and Beyond: The Wildlings
According to A Wiki of Ice and Fire the A World of Ice and Fire mobile app states that the island they go to is Skagos though this is a semi-canon source.