Pam,
Good for your sticking to your guns. With the help of Jim and Mary Ann, I think we've got the parents of Robert Baker Liverpool

Robert b 1837 s/o MathiasCatherine was with his parents in the 1861 census--THANKS, Mary Ann
1861 DouglasCensus
Cain, Catherine, head,widow, F, 46, 1815, shopkeeper, Braddan
CAIN, ROBERT, son, unmarried, M, 23, 1838, BAKER Douglas
Cain, Thomas, son, unmarried, M, 21, 1840, baker, Douglas
Cain, Catherine, daughter, unmarried, F, 16, 1845, dressmaker, Douglas
Cain, John, son, unmarried, M, 13, 1848, scholar, Douglas
Cain, Joseph, son, unmarried, M, 11, 1850, scholar, Douglas
Cain, Matthew A, son, unmarried, M, 8, 1853, scholar, Douglas
Cain, Richard A, son, unmarried, M, 6, 1855, scholar, Douglas

He was not with his parents in 1871 census.

We know your Robert md Ann Kennedy 19 Jun 1861 Braddan

Our other candidate was still with his parents in 1871 Census
Robert b 1838 was with his parents in
1871 Douglas Derby Square
Edward 68 retired business, Elizabeth 63, Robert 32 baker

Given the above together with the naming of Robert/Ann's children I would say there is a high probability that your Robert is s/o Matt and Catherine.

Unfortunately, Catherine Craine Cain(e)'s will that we have only concerns the administrative aspiects of her will rather than the content.
It does note that Thomas, the next son after Robert, was made executor of her will. If Robert were still in IOM, he likely would have been named executor--makes sense that he is probably your Robert Cain(e) baker of Liverpool.

If someone has access to Manx wills, Catherine died 10 Dec 1895 Douglas and her will is in the 1896 Douglas Wills
Mormon film #CAIN, Catherine 1896 Dgs 8 0106523

Hopefully, the will content will clarify that this is your Robert. At a minimum, the will should note if he was "off island" or better yet, in Liverpool.

DJD