Are you thinking about primogeniture? The Mongols actually practiced ultimogeniture, meaning that the youngest son would inherit whatever the parents left behind. As a result, Tolui inherited most of Genghis Khan's personal possessions

As for becoming khan, the Mongol nobles elected their khans in kuriltais. Ogedei had the support of Genghis Khan, but he was not automatically voted in. Tolui ruled as regent for 2 years before Ogedei assumed the throne. In any case, Genghis Khan himself had ruled out Chagatai by saying that he was obstinate and that Ogedei would be a better choice

In any case, Chagatai's obstinacy served him well. I believe he was the only son of Genghis Khan to not die of alcoholism or something related, and Chagatai was often reliable in executing legal matters