What is the Shariah ruling regarding a married man allowing his sisters and wife to travel with a foreign driver without a mahram, and to spend the night outside the home, and to travel abroad (Dubai, Egypt, and Turkey) alone or with a non-mahram, bearing in mind his justifications which include his trust in them and his busy schedule?

A woman is not permitted to travel without a mahram (definition) (unmarriageable kin) except in cases of extreme necessity. It is also not permissible for a woman to be in khalwa (definition) (seclusion) with a non-mahram man, such as being alone with a driver, even if the car is driving on crowded streets. A man must be accountable before Allah for those under his care and protect them from causes of temptation and evil.