Is it permissible for the husband to rent a private car to transport his wife and two daughters to their gymnastics training, with him handling communication with the driver and paying the fare, given that the wife cannot use public transportation due to having an infant with her?

Many contemporary scholars believe it is impermissible for a woman to ride in a car with a foreign driver unless there is someone present who negates the state of khalwa (private seclusion). The presence of two young daughters does not negate khalwa, because the presence of someone who is not a source of shame due to their young age is considered as if they are absent. Therefore, either the husband should take the girl by herself, or he should accompany her in the car, or someone whose presence negates khalwa should be with her. If this presents difficulty, and the fitna (temptation/strife) is secure, and the road is bustling with passersby, then it is hoped that you may act upon the opinion of those who permit riding with a driver when fitna is secure and suspicion is dispelled.