Greg, in my last message you will see that there appears to have been a transcription error with the inscription on the gravestone for Robert Corkill. The day and month were the same as the burial entry, but the year should have been 1875 not 1885.
1875 (confirmed by Brian with the census entry), plus other censuses, identifies him as Esther's widower, a farmer of 8 acres living in Ballakilley, Maughold. His daughter Margaret Woods was living with him.

We need the place name and other details from the Maughold M.I. to find out more about the other possible parents of Robert b.1819/1820: Peter Corkill & Elinor Clague.

All we know for sure is that this Robert Corkill in the 1861 census fits with the USA information you gave for him:
1 76 Cott on Dreemskerry Robert CORKILL Head MAR 41 Blacksmith Maughold
1 76 Cott on Dreemskerry Catherine CORKILL Wife MAR 42 Bride [QUAYLE]
1 76 Cott on Dreemskerry Esther CORKILL Daughter UNM 19 Servant maid Maughold
1 76 Cott on Dreemskerry Robert CORKILL Son UNM 17 Blacksmith Maughold [went to USA?]
1 76 Cott on Dreemskerry Catherine CORKILL Daughter UNM 16 Maughold
1 76 Cott on Dreemskerry John CORKILL Son UNM 12 Scholar Maughold
1 76 Cott on Dreemskerry Ann CORKILL Daughter UNM 9 Maughold
1 76 Cott on Dreemskerry Eleanor CORKILL Daughter UNM 7 Maughold
1 76 Cott on Dreemskerry Edward CORKILL Son UNM 4 Maughold
1 76 Cott on Dreemskerry Isabella Margaret CORKILL Daughter UNM 1 Maughold.

You wrote about an adoption? Some USA censuses record "mother of how many children" - I don't know whether this identifies adoptions? Obviously you need to find out if you are looking for a blood line.

Sue