Summary of answer:
Praise be to Allah
If the matter is as you describe, that you wrote these messages to your wife without intending that divorce should happen – rather it was with the intention of threatening or scaring her – then no divorce has taken place, as has been explained previously in fatwa no. 72291.
If a woman claims that her husband has divorced her, and the husband denies it, then what counts is his word, unless the wife can produce proof, which is two witnesses of sound character, as has been explained in detail, with mention of the scholars’ views, in fatwa no. 175181.
Thus it is known that your wife is still married to you, and is not divorced from you, based on what you have mentioned.
So what she must do is fear Allah, may He be exalted, and comply with the rulings of sharia, which indicate that what counts with regard to whether there was an intention that divorce should happen or not is the word of the husband, as we have explained above.
If the wife is uncertain about her situation, or she is uncertain as to what her husband says about any of the details of what happened, or she herself is not content with what you say concerning this issue, then undoubtedly the only proper thing to do in such situations is for you and her to go to a scholar whose knowledge and trustworthiness you both accept, and tell him what happened between you, and accept his verdict and fatwa concerning your case.
This woman should understand that if she marries somebody else in this situation, then she will be committing an immoral deed, because she is still married to her first husband and has not become separated from him.
In that case, the fatwa of the person whom she asked will be of no benefit, even if he is a scholar, because he gave an answer concerning an abstract issue, without hearing both sides of the story.