by Helen Robertson, Scottish Historian
If Sarah’s line does come down through Isabel (William the Lion’s daughter) who married Robert de Ros in 1191, then her line is not through Ermengarde but through William’s mistress (also Isabel) the daughter of Robert de Avenel, Lord of Wark and Tweed.
In 1183, Isabel, William’s natural (or illegitimate daughter) – married Robert de Brus (Third Lord of Annandale). Robert died around 1190 leaving Isabel a widow (without children), and one year later in 1191 she married Robert de Ros, Lord of Wark and Tweed.
in 1183, Margaret, William’s natural (or illegitimate daughter) – married Eustace de Vescy, Lord of Alnwick
In 1184, Ada, William’s natural (or illegitimate daughter) – married Earl Patrick of Dunbar (my Cospatric line)
the above shows William on a flurry of marriage arrangements – perhaps before he proposed to Matilda, see below!
In 1184 the still unmarried William the Lion proposed to Matilda, daughter of the Duke of Saxony. Matilda was a descendant of Edith (daughter of Malcolm Canmore) who was Matilda Queen of England – the Pope refused permission on the grounds of consanguinity.
in 1186 William eventually married Ermengarde, daughter of Richard Vicomte de Beaumont, the son of an illegitimate daughter of Henry 1 king of England. The couple had two legitimate daughters (confusingly named Margaret and Isabella) before the birth of their son and sole heir, Alexander, who was born on 24 August 1198.
Incidentally, it is thought that William spoke only French and not English or Gaelic, and he was surrounded by a French speaking court during his reign as a Scottish king! That is suggestive that Countess Ada and his siblings also spoke French.
The above information is accurate, taken from primary source records.