What is the ruling on a wife going to a beauty center where men work, but the women's section is isolated from men, and there is no mixing?

It is permissible for a woman to go to beauty centers if several conditions are met, including: that the worker is a Muslim, that there is no exposure to men or cameras, that the beautification does not involve forbidden acts such as plucking eyebrows (namṣ) or imitating disbelieving women or dyeing hair black, that private parts are not exposed or touched, that the husband gives his permission to his wife, and that there is no extravagance. Sheikh Ibn Uthaymin was of the opinion that women can style each other's hair at home, to save money and avoid religious prohibitions.