As has been commented, from Arthur's marriage, his mother's maiden name is certainly not Davidson. Have you got a sharper image of this cert? If not, you can contact SP and they can send you an enhance image which often help enormously where writing is hard to make out.
However, if Arthur was being creative with his parents' names to cover illegitimacy, what shows on his wedding registration for mother's maiden name and father's details are irrelevant.
You mention that you found (looking for?) the cert from 1921 which showed mother as Mary Stevenson. I am confused by something. The 2 birth certs you mention, do they both show the birth date of 11 December 1921 and mother Mary Stevenson? What about the time of birth on the day? Other details?
There is only though one birth in Midlothian. Where was the other one you are discussing?
Monica
