Considering that a non-religious Jewish man cannot be considered as a second man to permit yichud (according to some opinions), may a religious Jew be together with a lady if he is accompanied by his non-religious Jewish father?
According to those who say that a porutz (a person who isn’t careful with the laws regarding separation of men and women) is not considered a second man, the reasoning would be that it would then be like yichud between one man and one woman which is forbidden. As the reliable person will not be afraid of being promiscuous in front of the porutz. On the other hand there are those who question this. See sources.
This is all theoretical because although there is controversy about yichud with one kosher and one porutz, the halacha is that it is permitted.
See Dvar Halacha 9-5 who brings the various opinions, also see ftnt. 5 that he asks your question; If we say that the son will be embarrassed from his father, or since he is a porutz he won’t be embarrassed. He does say that in the opposite case, if the son is the porutz, then the Tzemach Tzedek says that is will be yichud because the son won’t be embarrassed in front of his father.
Pischei teshuva E:H 22-4, Maharshal Kiddushin 4-21, Shevet Halevi 5- siman 202-1, Pesach Habayis 5-3, Toras Hayichud 3-4, Dvar Halacha 6- ftnt 12 in th name of one of the gedolei hador,