Is it permissible for my wife to have her baby delivered by a male doctor for fear of giving birth with a female doctor who previously caused the death of a woman?

It is not permissible for a woman to expose her 'awrah to a non-mahram (definition) man except out of necessity or severe need, such as illness. In such a case, one must seek a skilled Muslim female doctor. If none is available or she is not skilled, then a non-Muslim female doctor. If none is available or she is not skilled, it is permissible to go to a trustworthy Muslim male doctor, preferably in the presence of her husband, one of her mahrams, or reliable women to prevent impermissible seclusion (khalwa (definition)). The mere apprehension of the wife does not justify going to a male doctor unless it is proven that the female doctor is unskilled or unqualified. Childbirth is considered an easy process that can be performed by midwives and female doctors, and male doctors should not be resorted to except in cases of true necessity, such as difficult labor.