Máel Coluim ("Malcolm") mac Alexander was the illegitimate son of David's older brother, Alexander I. According to historian Orderic Vitalis, Malcolm "affected to snatch the kingdom from [David], and fought against him two sufficiently fierce battles; but David, who was loftier in understanding and in power and wealth, conquered him and his followers."
Malcolm escaped into more obscure parts of Scotland, surviving and gaining allies over a six-year span, after which he attempted to attack David for the throne again. One reason for his motivation might have been that David spent time in England, seeming to prefer visiting Henry's court over being among his own people.
Malcolm, with the support of Óengus of Moray (mentioned here), marched against David's army. The Annals of Ulster report that 4000 of Óengus' army and Óengus himself died, while only 1000 of the men loyal to David died that day. David's force, led by a constable, marched into the now undefended Moray and captured it. Malcolm himself escaped, and spent the next four years battling David's forces.
David was aided with a large force, including ships, from Henry. Malcolm was captured in 1134 at Roxburgh Castle, and history has no more to say about him. Moray was given to David's nephew, only son of David's oldest brother Duncan, who had held the kingship for less than six months in 1094.
David was called by William of Newburgh a "King not barbarous of a barbarous nation." He attempted to make some reforms that he felt Scotland and its church needed. I'll explain some of those tomorrow.
