I'm wondering if Adam saw one draft of his father's will and thought it was the final one. However, because the father also loved Jenny (adopted or not) he elected to keep things split between Adam and Jenny just to prevent him from taking The Richards' Companies and, especially, The Academy in directions that the father would've severely disapproved of.
In the initial confrontation between Adam, Susan, Jenny and MC, Adam tries to tell Jenny that he's trying to continue their father's vision of the Academy but Jenny stops and corrects him saying that it's HIS vision for the Academy and to leave their father's name out of it.... That tells me that whatever Adam wants to do is something that the entire rest of the Richards family will severely frown upon, maybe worse. Why else would he need to have Theo around as a bodyguard all the time.... Jenny, at this point has just as much power and influence with the Academy, yet she has no need of bodyguards. It also seems to say that every other member of the family, Richards and Miller would attempt to oppose Adam using every means they have... and I'd bet Jill and her family would help support Jenny's efforts, as would Mr. White and his daughter......