Sorry I didn't see this post until just now, and I notice you have already added Jean Maxwell as John's mother, but I am going to mark that as uncertain pending further investigation.
Unfortunately the source you are using, like many generic FamilySearch databases is "based upon data collected by the Genealogical Society of Utah" and not necessarily from original parish records. In fact the marriage record of John Maxwell and Barbara Stewart, doesn't mention his parents or the name of her mother. Although this is a transcription of the Canongate register of marriages, I have confirmed that this is all that is written in the register.
The Complete Baronetage, vol. 4, p. 313 does state that Jean Maxwell, daughter of John Maxwell of Southbar, was the mother of John Maxwell, 2nd Baronet, but would like to be able to confirm that with primary sources if possible.