See Fasti Ecclesiae Scoticanae, iv, p. 202 for his article. He was married twice more, 2 Mary ANDERSON & 3 Rachel, dau Colin ADAMS, min. Anstruther Easter - with further issue.
The article in Fasti for his father vol V, p. 304 states mother of his kids to be Lucrece CAIRNCROSS [It has a comment – ‘he is said to have m Eliza dau Jno SINCLAIR, dean of St. Andrews’]. You quote the DNB article which also has Lucrece. One of his daughters was Lucrece.
Do you have some overwhelming evidence to counteract both of these publications?
If not then why have you got his mother as Elizabeth SINCLAIR??
And somehow an additional given name appears to have been invented for him. He only appears in things I've seen as plain old Alexander, yet we have Andrew Alexander. This creativity baffles me; obviously I'm greatly disadvantaged by not going to a Montessori or some such.