Where did the evidence for the Scotland connection come from? And the information that Emma's maiden name was also Swanson? She is certainly living in Monroe country from 1900 onwards but what record do you have showing she was born there?
This may seem picky but it is very easy to spend a lot of time going down a false path (e.g. trying to track down A. B. Swanson and then he turns out not to be related at all), so you need to get as much concrete evidence about Emma's life as you can before looking at potential parents.
Here is Emma in the 1900 census, already widowed. Both parents listed as born MS.
https://www.familysearch.org/ark:/61903/1:1:M9XK-KFBFive living children out of seven. Three in household with name Swanson - eldest Braetan (indexed Bractan) Swanson aged 20, Charley being the youngest. One McNary child in household - Pearlie McNary, aged 11. One Amelia Robertson, aged 3, confusingly also listed as a daughter (perhaps married a Robertson then divorced and reverted to McNary?)
https://www.familysearch.org/ark:/61903/1:1:MPDH-Q9C - in 1910, similar mix of children/grandchildren. Born MS, parents born MS.
https://www.familysearch.org/ark:/61903/1:1:MNTS-8R4 - George Swanson in the next census with mother Emma now "Emma Arvard" (born Georgia, parents born US in this census). Details are off so perhaps she didn't give the info on this one.
This may be Charley's death in Ohio - gives his parents as Charles Swanson and Emma Coolidge
https://www.familysearch.org/ark:/61903/1:1:X6P8-WDM1892 school records for some of the Swanson children, mother listed as Emma Cooler?
https://www.familysearch.org/ark:/61903/1:1:QK64-92JHIn this they seem to be listed in Marion county.
I think the first area to concentrate on would be finding marriage records for Emma, and her death certificate to see if one of her children knew her parents' names. Also birth, marriage, and death records for her known children to see if there are any that list her maiden name.