The nearest I could find just now on Ancestry in 1851 was:

HO 107/ 2524 f.401 p.15 sch.55
Laxey Glen North, Lonan (District 1)
Robert Kelly, head, mar, 33, miner in Laxey lead ore mines,
Ellen, wife, mar, 26,
John J, son, 2,
William, son, 8mo.
All born Lonan, IOM

But they are all still there with more children in 1861 so seems not yours. Might turn out to have some connection tho’.

Have you tried searching with the names of any children alive in 1851 and 1871?