Has divorce occurred between the mother and father three times, based on the mother's doubt about the first pronouncement, and the definite occurrence of the second and third pronouncements?

It appears that the questioner's father uttered the word "divorce" three times. If the first utterance was "You are divorced," it is an explicit divorce. However, if it was "That's it, I'm going to divorce you," then it is a promise of divorce, and nothing is binding from it. The second divorce, with his statement "You are divorced for the third time," makes the wife unlawful for him according to the majority of scholars until she marries another husband. As for the third divorce, it occurred after the marital bond had been severed, so it is null and void. It is not permissible for your father to continue cohabiting with his wife.

According to the madhhab (definition) of Ibn Taymiyyah, uttering "divorce" three times in one phrase counts as a single divorce. If the father took her back before the 'iddah (definition) (waiting period) expired, then the third divorce would be considered a second one. However, if he did not take her back after the first divorce, she has become irrevocably separated from him, and he can only remarry her with a new marriage contract.

It is advisable to consult trustworthy scholars directly to elaborate on the matter and act upon their fatwa (definition).