Your premise is that women don’t know how to drive, and that is the problem?
– – no, my premise is the concern for women working with men in close quarters, and traveling together in the small ambulance back and forth to the hospital. At the same time, the patients are more sensitive to who examines them. In all seriousness, this may work. A call goes out, woman or girl patient, a woman with medical training goes to the scene (of course whichever EMT arrives first will begin the evaluation) and after the exam and the patient is loaded to the ambulance, the woman EMT can leave.
Also, if we are concerned that the ambulance crew may hesitate to take a call on Shabbos if they are not going to return home, shouldn’t we also be concerned that a woman may not want to call Hatzala if she will be treated and examined by men? This is a very real situation. I know at least one young mother, with a high-risk pregnancy, and travelling from the Rockaways to a Manhattan hospital, who said if she went into labor on YomTov she planned to call a car service rather than Hatzala.