What is the ruling on joining social clubs and going out for recreation there, given the mixing and immodesty that occurs, even while being careful to go at times when it is presumed that there will not be many transgressions?

If clubs involve mixing between genders, immodest display, and other Sharia-prohibited matters, then it is not permissible to subscribe to them or visit them during times when these reprehensible acts occur, because it falls under cooperating in sin and aggression. However, if they are free from such reprehensible acts, there is no harm in visiting them. A man must be responsible for his family and protect them from reprehensible acts. The dayyuth (pimp/cuckold) who condones indecency among his family will not enter Paradise.