Well, that's an odd and even dangerous method of succession. Usually kingdoms tended to adhere to a very clearly delineated order of succession to avoid destabilizing the country and/or bloodshed. (Which didn't always work either, a well-known example of a succession conflict is War of the Roses.) One of the most common methods in high middle ages was eldest son inheriting all. Other older methods included splitting the realm amongs male sons, which is how the Carolingian Empire fractured apart (establishing what would eventually eveolve to France and Germany).
Unless this is their normal - and it appears it isn't - the kingdom would do well to ignore the late monarch's request and stick to the established succession. Trying to dictate your heir often leads to strife.
Or one could go the Crusader Kings way and try to get rid of that low-stat, negative-trait heir so that high-statted god of war is your new heir (and then he dies of pox).