Given the following context:

The period between the accession of David I and the death of Alexander III was marked by dependency upon and relatively good relations with the Kings of England. The period can be regarded as one of great historical transformation, part of a more general phenomenon, which has been called "Europeanisation". The period also witnessed the successful imposition of royal authority across most of the modern country. After David I, and especially in the reign of William I, Scotland's Kings became ambivalent about the culture of most of their subjects. As Walter of Coventry tells us, "The modern kings of Scotland count themselves as Frenchmen, in race, manners, language and culture; they keep only Frenchmen in their household and following, and have reduced the Gaels to utter servitude."This situation was not without consequence. In the aftermath of William's capture at Alnwick in 1174, the Scots turned on the small number of Middle English-speakers and French-speakers among them. William of Newburgh related that the Scots first attacked the Scoto-English in their own army, and Newburgh reported a repetition of these events in Scotland itself. Walter Bower, writing a few centuries later about the same events confirms that "there took place a most wretched and widespread persecution of the English both in Scotland and Galloway".
The first instance of strong opposition to the Scottish kings was perhaps the revolt of Óengus, the Mormaer of Moray. Other important resistors to the expansionary Scottish kings were Somerled, Fergus of Galloway, Gille Brigte, Lord of Galloway and Harald Maddadsson, along with two kin-groups known today as the MacHeths and the MacWilliams. The threat from the latter was so grave that, after their defeat in 1230, the Scottish crown ordered the public execution of the infant girl who happened to be the last of the MacWilliam line. According to the Lanercost Chronicle:

answer the following question:

What kin-group's threat was so grave that a child was executed? 

MacWilliams