Is the wife considered divorced after the husband utters the divorce pronouncement three times, taking into account his anger in the first two instances and his full awareness in the third, and is his statement valid that the divorce does not occur if that was not his intention?

We understand from your answer that the divorce of an angry person is effective if he is aware of what he is saying, and that the first two divorces you mentioned are undoubtedly effective. As for the last divorce, your husband's statement that he did not intend divorce is incorrect, as an explicit divorce does not require an intention to occur, according to Ibn Qudamah: "An explicit divorce does not require an intention; rather, it occurs without purpose, and there is no disagreement on this."

Sheikh Ibn Uthaymeen supported this opinion by saying: "If divorce occurs from its rightful person, then it occurs explicitly even if he did not intend it," likening it to buying and selling, adding: "Whenever you find separation like buying, selling, leasing, and gifting, if it occurs from a person, even if he did not intend it, as long as the wording is present."

Regarding the divorce of a jester, Ibn Uthaymeen said: "As long as the word of divorce is uttered by a sane person, who is rational and discerning and knows what it is, his saying: 'I did not intend for it to occur' is not up to him, but up to Allah. Furthermore, logic dictates this, because if we were to adopt this matter and open the door, everyone would claim this, and no divorce would remain on earth."

If you do not feel safe from your husband's attempt to circumvent the law to take you back in a way that is not permissible by Sharia, then the correct action is what you did by raising the case to the Sharia court. Its ruling on the matter is final, and it does not accept intention in an explicit divorce. If the court rules for divorce, it is considered effective from the day the husband pronounced it, and the waiting period ('iddah) begins from that day.