Does divorce occur in the two previous instances—the first under duress and the second after intercourse—and is it permissible to take the wife back after the current third divorce, or has she become irrevocably divorced?

A coerced divorce does not take effect if its conditions are met, but placating one's wife is not considered coercion. An explicit pronouncement of divorce causes it to take effect, even if one did not intend for it to take effect. If you explicitly pronounced divorce twice, then two divorces have become binding upon you. As for a divorce by innuendo, it does not take effect except with intention.

Divorce pronounced during a period of purity (Tuhr) in which intercourse occurred is valid according to the majority of scholars, and this is the preferred opinion. As for purity from ritual impurity (Janabah), it does not affect the validity of the divorce. If three divorces have occurred, your wife is not lawful for you until she marries another husband. If it is less than three, you may take her back during her waiting period ('iddah), or with a new contract after the 'iddah expires.