I am researching these families in the Northumberland area. On various records they mention Alnwick, Norham, Murton, Goswick, Kyloe, Berwick Upon Tweed. Upon initial searching it seems that these places are close to one another. Please correct me if I am wrong. I have the following information from generous volunteers and records that I have found myself.

These I am sure are connected:

Marriage:
Andrew MATHER to
Martha RICARBY
21 May 1809
Norham, Northumberland
IGI Batch#M000761

Births:
Golden Square Presbyterian, Berwick:
March 10, 1812, Robert son of Andrew MATHER a husbandman at Murton and Martha his wife. Born at Murton aforesaid.

April 8, 1814, John son of Andrew MATHER and Margaret his wife of Goswick, Holy Island Parish, born March 27.

March 7, 1816, Elizabeth daughter of Andrew MATHER a servant with Mr. Weir at Goswick and Margaret his wife. Born February 19.

They had at least two other children who were born in Aberdeen, Scotland:

James MATHER born about 1820
George MATHER born 1822
Isabella MATHER born 1824

They are all listed in the 1841 census for Woodside Parish, Aberdeen:
Address: Lower Middlefield
Andrew MATHER 60 Farmer b.England
Martha " 60 b.England
Andrew(jr) " 30 Ag. Lab.(he is Robert,never marries)
Elizabeth " 25 Servant(she marries Alex.MIDDLETON)
Margaret " 20 Servant(think she is James wife)
James " 20 Millwright App. b.Aberdeenshire
George W. " 15 Ag. Lab. b.Aberdeenshire(moves to US)
Isobel " 15 Servant(unknown what happens to her)

The son John b.1814 is out of the home and marries in 1842 to Anne CONNON. They move back to Northumberland by 1846 and sail to U.S. in 1854.

I think that the father, Andrew MATHER may be one born 4 April, 1779, to Andrew and Margaret MATHER of Fenham East Steads, Baptised at Holy Island. They also had the following children:
Mary MATHER baptised:1777 Holy Island
Eleanor MATHER baptised:1781 Holy Island
Elizabeth MATHER baptised:1784 Holy Island
John MATHER baptised: 1787 Holy Island

I found the death of a Margaret MATHER which may be Andrew's wife:
Parish Records:Burial
Margaret MATHER
Abode: Mounthooly Kyloe
Died: 16 Dec, 1800
Age: 46
Husband: Andrew(laborer)
Place: Belford, St.Mary
Northumberland, England

I found a marriage record on the IGI which may be this couple:
Andrew MATHER to
Margaret RIDPATH
13 June, 1776 Holy Island, Northumberland
Batch#M002561

Any help or input appreciated.
Thanks,
Margaret