Thanks to you both. As mentioned previously, his age is what does concern me. On his Death Record is could be 73 or 78, and on the records from Deceased Online, it says 73. I have learned from experience that the information given by living relatives can be incorrect at times, especcially since they are typically grieving at the time the information is given. I am leaning towards he is the son of James Hacket and Barbara Chalmers, but the fact he is not even mentioned in their wills is bothersome, but it could explain why his parents were not listed in his Death Record.
In looking at the Deceased Online data, Alexander and his 2nd son James is buried at Rosehill, along with Alexander's wife Ann Lyall Hackett. This innformation was listed in her Death Record. Ann and George are buried at Churchyard Cemetery, along with James' daughter Agnes. In the Deceased Online Data from Rosehill, James is listed as Hacket and says he was buried at No. 22 11, Class A, Sec. 100, Depth 5, and was owned by Alexander Hacket.
If you would like to see what information I have, it is located at http://www.ourfamilygenealogies.com/FamilyTree/13091.htm
The Captain Alfred Alexander listed here is my Great-Great Grandfather. If you wish to correspond directly, my information is on the main page of the site.