It already happened in OTL in the years 1440-1444 and 1492-1501 that Poland and Lithuania had separate monarchs from the same dynasty, but such situation had not lasted long. So POD is Jogaila had three instead of two surviving sons with Sonka (they already had 3, one just died as infant)-Vladislaus, Casimir and Alexander (born 1424, 1426, 1427). Vladislaus dies in Varna like IOTL, Casimir takes Lithuanian throne in 1440, Alexander is destined to join clergy, but after death of Vladislaus, he had better perspectives. OTL interregnum lasting 3 years would not happen IOTL with two Jagiellon candidates available, say Casimir can't reach agreement with Lithuanian magnates and bishop of Cracow, thus Alexander is elected, Poland and Lithuania once again are ruled by two brothers. Such situation could stick for decades, and maybe even continue in next generations with two separate lines of House of Jagiellon. How would situation develop? With monarch residing in Lithuania, could Grand Duke keep more power? Could Lithuania survive wars with Moscow hands without extensive Polish help? Poland would not be affected as much, initially at least-Lithuania did not participated in war against Teutonic Order, although question of election could be interesting without personal union of hereditary GDL and elective Kingdom of Poland, still, as long as there are royal sons around, election should be pure formality.