Nothing is clear about the father yet. Depending on his illness, he may be incapacitated and unable to perform any actions, and I don't think dying was part of his plan, so he probably wouldn't have left a will in case of any eventuality, especially considering what's said in Chapter 2 about him having little to inherit anyway.
Regarding the will, it's also possible that a company executive wants to take the company away from the Tanemori family. Of all the characters introduced in Chapter 2, Kazuomi's right-hand man was there, so he'll have some relevance in the future. The character who generates the most curiosity in this regard is Yuzu's mother; her perspective on this whole matter is the only one from Kazuomi's immediate family (wife and children) that we don't know.
Finally, and what I would most like to highlight from the chapter, is that this would break the last barrier on Naomi's part towards the Tanemori family; that innate dislike he felt for his father's other family should now disappear.