Remember when Zoro was buying swords in Loguetown we have learned about cursed swords being (chapter 97) . The swords customer Ippon-Matsu told about cursed swords. Many famous swordsmen of the past have suffered tragic deaths after carrying around the cursed swords.
However, Zoro defeated the curse of Sandai Kitetsu with his luck (or maybe his demonic nature or his own curse) and then customer said that the swords chooses it’s owner.
First I thought that Wado Ichimonji is cursed too and after Kuina had fought with Zoro with katanas instead of bamboo swords, Wado Ichimonji chose Zoro his owner for his demonic aura. And Kuina inevitably died a few hours after this fight.
The point is that the circumstances of Kuina’s death resemble the description of the deaths by a cursed sword. But now I think It’s not that simple, firstly because Wado Ichimonji is considered to be a noble sword as it seems, even the name of the sword indicates that (it’s Straight Road of the Harmony). The sword chooses it’s owner, but a noble sword should have a special kind of motives to change it’s owner as opposed to a cursed sword. A noble sword should be like a noble swordsman, remember Ryuma with his rule: whenever someone touched their sword sheath with his, even by accident, Ryuma would immediately take this action as a form of challenge for a duel to the death (Monsters one-shot).
Or remember the battle between Ryuma and Zoro: Zoro won, so Ryuma gave Shusui to him. Even then, I think Wado Ichimoji could chose Zoro as it’s owner. I can see two reasons: Zoro is a descendant of the true owner of Wado or he carries the same will as the true owner.
I tend to think that Kuina took Wado for a fight without father’s permission, and Wado never did belong to her. Remember that Koshiro said girls would never be the world’s number one and the fact that he doesn’t like girl to take over the dojo could mean that he would never allow her to have her own sword.