Eupheme seems no longer thought to be a daughter.
See PoMS, no. 5989 (https://www.poms.ac.uk/record/person/5989/; accessed 21 February 2021)
Christina was married first to William Bruce, lord of Annandale; later she was second wife of Earl Patrick (d.1232). On Countess Christina, see Andrew B.W. MacEwen, ‘Seven Scottish Countesses: A Miscellany. III. Christina de Brus, Countess of Dunbar’, The Genealogist, Fall 2003, 223-33. Christina was first wife of William de Brus, who died × 1212; and secondly wife of Earl Patrick (I) of Dunbar, who died in 1232. Christina was thus the stepmother of Earl Patrick (II). MacEwen suggests persuasively that Countess Christina was a daughter of Walter son of Alan (I) the steward and a sister of Alan the steward. This is based on the evidence that Birkenside (BWK), which was held by Walter son of Alan the steward, was later part of the marriage portion of Countess Euphemia, wife of Earl Patrick (II) [see 3/15/74 below]. MacEwen suggests that Christina inherited Birkenside from her putative father, Walter son of Alan (I), and that Euphemia was her daughter with William de Brus.
Thus, Christina, who married secondly Earl Patrick (I) of Dunbar, apparently had a daughter from her previous marriage, Euphemia de Brus, who married Earl Patrick (I)’s son from a previous marriage, Earl Patrick (II). Thus Countess Christina appears to have been both stepmother and mother-in-law to Earl Patrick II. See also Andrew B.W. MacEwen, ‘A Clarification of the Dunbar Pedigree’, The Genealogist, vol. 9, no. 2 (1988), 229-41
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http://fmg.ac/Projects/MedLands/SCOTTISH%20NOBILITY.htm#PatrickDunb...
He left on Crusade with Louis IX King of France in Nov 1247 but died en route[1560]. Matthew Paris records the death of "comes Patricius qui inter magnates Scoitiæ potentissimus habebatur"[1561]. The Chronicle of Lanercost records that "…magistri Patricii" died "apud Marsilium"[1562]. m (1213 or before) EUPHEME, daughter of [WILLIAM de Brus of Annandale & his wife Christine ---] (-1267). "Eufemia comitissa" donated revenue from land in "Kirkinfyde" to Dryburgh monastery, for the soul of "domini mei Patricii comitis", by undated charter[1563]. Her parentage is suggested by MacEwan[1564]. If correct, she was her husband’s step-sister, daughter of his father’s second wife by her first husband. The Chronicle of Lanercost records the death in 1267 of "domina mater domini comitis Patricii de Dunbar, Eufemia…magistri Patricii qui apud Marsilium obiit"[1565]. Earl Patrick & his wife had two children:
a) PATRICK de Dunbar ([1213]-
b) WALTHEOF [Waldeve] (-after 3 Feb 1245). Rector of Dunbar.
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Euphemia, countess of Dunbar
Curator Note from Anne Brannen (11/14/2019):
The Peerages give the wife of Patrick Dunbar as Euphemia Stewart; MedLands gives her as Euphemia de Brus.