If there is any connection between the two families I don’t think it is close. The Hashemite family for a long time ruled the Mecca-Medina region of Arabia, until they were kicked out by the Saudis. Fortunately for the Hashemites the British had given them Transjordan and Iraq to rule by then. (They lost Iraq in the 1958 revolt.) I think the Saudis came from a different part of Arabia to begin with.
True, but the overthrowing of the Jordanian king in favor of Islamists would set a precedent. The monarchs of the region are supposed to have divine right to rule without question. If the king of Jordan has no legitimacy, it would embolden revolutionaries throughout the region to end the reign of the kings.