Can't help with the missing children as yet, but I can add a bit more to the story.
John Mitchell senior was born on 22 Sep 1818 in New Deer, to John Mitchell and Elspet Keith.
He was married three times. His first wife was Elizabeth Fyvie, who he married on 29 Nov 1846 in Aberdour. They had one son, William, who was born in 1847 in Aberdour. Elizabeth must have died soon after that, as John Mitchell is a widower in the 1851 census in Tyrie. William is with his maternal grandparents in Aberdour.
He married his second wife, Margaret Watt, on 21 Jan 1853 in Tyrie. They also had one son, John, born 2 Mar 1857, Pitsligo (Rosehearty). John senior, Margaret and John, along with elder son, William, are together in Rosehearty in the 1861 census. By 1871, William has gone, and only John senior, Margaret and John junior are in the house - along with Jessie McWilliam, domestic servant, who John senior goes on to marry in 1873, after Margaret's death.
John Mitchell junior, who was also a tailor - the half brother you mention, who brought his remaining siblings to Quarriers - married his cousin, Margaret Mitchell on 11 Oct 1878 in Monquhitter. Margaret was the daughter of William Mitchell (also a tailor) and Jane Watson - William was John Mitchell senior's younger brother. John and Margaret did, indeed, live in Cruden - they're in the 1881, 1891 and 1901 censuses in Cruden, along with their children.
Ruth