All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the husband writes the divorce of his wife and intends divorce while doing so, then his divorce takes place as clarified in Fataawa 89894 and 87034.
It appears that you wanted to divorce her while writing the words of divorce as you said: “I sent her divorce in writing as a last resort…”
Moreover, three times divorce with one wording in one session takes place as three divorces according to the view of the majority of the scholars among whom are the four Imaams, and this is as well the view we adopt in Islamweb. For more benefit, please refer to Fataawa 83467 and 82330.
Therefore, your wife becomes irrevocably divorced from you and she is unlawful for you until she marries another man a true marriage, and he consummates the marriage with her, and then he dies or divorces her.
Indeed, you hastened (to divorce her) while you had the time to resolve the matter gradually. If a wife becomes disobedient and rebellious towards her husband, there are some steps in Islam that the husband should take to treat her, and divorce is the last solution. Even if you thought that divorce was the solution, you should have divorced her only once. For more benefit, please refer to Fatwa 85402.
As regards your daughter, we advise you to be wise in dealing with her, and both of you should endeavor not to make this divorce have a negative effect on her.
Allaah Knows best.