Is marrying one's sister legitimate and acceptable to God, given her questions about its invalidity and her refusal to return to her husband, especially after he had divorced her twice previously and threatened to take her children, knowing that he is an adulterer and an alcoholic?

If the husband divorced your sister with the second pronouncement of divorce and did not take her back until she gave birth, then she is irrevocably divorced from him with a minor separation (baynunah sughra). It is not permissible for him to take her back except with a new contract, a new dowry, and her consent, because the waiting period (iddah) of a pregnant woman ends upon her delivery. If he marries her with a new contract and a new dowry, and the rest of the conditions for a valid marriage are met, then she is his wife. Otherwise, she is not his wife. She should refer her case to the Sharia court to handle their separation and consider the matter of child custody.