Does a divorce uttered with the intention of escaping a humiliating situation, and without the speaker's intention for the divorce to actually occur, take effect?

Divorce pronounced under duress is not valid if the duress is considered legitimate, such as a threat of death or severe harm. It appears that you were not coerced into pronouncing the divorce, but rather you uttered it to get rid of your wife's troubles. Therefore, this divorce is effective. If it was the first or second pronouncement, you may take her back before her iddah (waiting period) expires. If it was the third pronouncement, she is irrevocably divorced from you, and you cannot take her back unless she marries another man and he then divorces her or dies, and her iddah ends. She must repent for her threats of death, and efforts should be made to reform her.