Is a mother sinful because she gave birth with the assistance of a male doctor due to the unavailability of a female doctor?

If a woman is genuinely compelled to have a man assist in her delivery, there is no sin in that. This is based on the general meaning of Allah's saying: (But whoever is forced, neither desiring [it] nor transgressing, there is no sin upon him), and His saying: (So fear Allah as much as you are able).