I’m not sure if any of this will help. I think this is the likely baptism for Andrew
Andrew Rutherford
Birth 22 Dec 1780 County Durham
Baptism 28 Jan 1781 Ebenezer Chapel, Swalwell, Wickham,
Denomination Presbyterian
Father John Mother Mary
No baptism for Isabella in Kelso but more than one in the county, the nearest to Kelso
might just be a coincidence and there was another there in 1786, parents William & Margaret.
Isabel Wilson
Baptism 22 Aug 1784
Father William Wilson Mother Janet Rutherford
Residence Sprouston, Roxburgh, Scotland
No marriage for Andrew & Isabella
John Rutherford Birth 4 Jan 1809
Cornhill, Northumberland Baptism 19 Mar 1809
Father Andrew Rutherford Mother Isasbella Wilson
Alexander & Isabella Rutherford both baptised 13 Mar 1815, Newcastle.
Colin