Is the mother's marriage considered Islamically valid, taking into account that the father divorced her three times: the first while she was menstruating, the second while she was pregnant, and the third with the phrase "You are divorced, divorced, divorced," and each time the divorce occurred in a state of extreme anger reaching the point of unconsciousness and unawareness, and was intended as a threat?

The fatwa accepted by us is that the divorce of a menstruating woman and the divorce of an angry man are valid and effective, unless the angry man completely loses his sanity.

If your father divorced your mother with three pronouncements of divorce while he was in control of his faculties and not overwhelmed, then his divorce is effective, even if he was extremely angry.

However, if he uttered the divorce while in a state of severe anger that completely deprived him of his reason, then his divorce is not effective.

Since the matter involves details, and you have consulted trustworthy scholars who issued a fatwa stating that the divorce did not occur, there is no blame upon you for acting upon their ruling.