I think you have two separate families. If you look at the 1837 Pigots Directory in Manx Notebook you will see Edmund Quine at Ballig Onchan and Edward at Ballalig Braddan, Douglas is in between.
It looks like John Quine was buried 1833 age 60 in Brian Lawson's index and could be the son of Nicholas Quine and Alice Cottier.
Then look at www.old-maps.co.uk, search for Douglas and follow the arrows until you find Quines Hill then enlarge the picture, you will see Ballalig etc. Ballaslig is shown further down the road on the other side.
Len Faragher