Hi Retsina
Just picking up on some of your comments above:
I think you are on the right track though. Ann definitely had a sister Jean and also a brother Robert. I found the family in the 1841 census, with father Robert and 5 siblings, Jean is aged 25, but no mention of Ann...
There are quite a few King families in Beith in those years so without further details, I wouldn't necessarily assume at this time that this is Ann's family at this time without further checks on records.
...but no mention of Ann, so finding her living with a David King (not sure who he is as they are the same age?), and son William aged 1 is a definite possibility.
The 1841 census is the most limited in terms of info. No relationships within the household were given. Also, ages for those over 15 were supposed to be rounded down to the nearest five years. So in that 1841 census entry, Ann and David could be aged between 20-24. Ages for those under 15 were supposed to show at their actual age (or as actual as census ages ever are!).
The 1861 census that you mention, shows Mary White King as Jean King's mother:
Mary White King 79 head b. Beith
Jean King 46 daughter b. Beith (1851 gave Dunlop as her birth place)
William Young 20 boarder wright b. Beith
Address: Giffen, Beith
There is possily some family connection to that 1851 entry and farmer Thomas White.
In the absence of details so far on Ann King, maybe looking for Jean King's death reg might provide details on her parents.
Monica