I had tried positing this scenario earlier.
In 1112, Baldwin I of Jerusalem got married to Adelaide del Vasto, the widow of Count Roger I of Sicily, and mother of Roger II, by then in his majority. Baldwin was already married to the Armenian Princess Arda, back when he was Count of Edessa, but she was of no political value in Jerusalem, and so was confined to a convent. Sicily, on the other hand was wealthy and powerful, and Adelaide brought with her some knights and Muslim archers upon arriving in Palestine.
However, both Baldwin and Adelaide were pretty old, and unlikely to produce offspring at their age, so it would look as though Roger II was a shoe-in for the throne of Jerusalem.
Unfortunately for him, the marriage between Baldwin and Arda had not been annulled, so his third marriage was bigamous. As Arnulf of Chocques, the Latin Patriarch of Jerusalem had suggested the marriage in the first place, and had been deposed by a Papal Legate on behalf of Paschal II in 1115 for approving the bigamous marriage, along with accusations on his own part of simony and sexual relations with a Muslim woman, he could only regain his post by agreeing to annull Baldwin and Adelaide's marriage. Adelaide returned to Sicily, and died the following year.
Roger of Sicily never forgave this humiliation of his mother, and perhaps was seriously peeved at being deprived of the kingship of Jerusalem, and for this, denied military aid to the Crusader states thirty years later.
Now what if either Arda died of natural causes, or she was killed on Baldwin's orders, or someone in his service decided to take the initiative to kill Arda when she was in confinement? What would it mean for the future of the Crusader states if the future King of Sicily were to have crown of Jerusalem?