Is it permissible to visit a non-observant family, especially if I witness their son hugging and kissing a girl who is a stranger to him inside their home?

Firstly: It is not permissible to judge an entire family as disobedient merely because one of its members is not committed. Muslims are presumed to be righteous.

Secondly: It is permissible to visit relatives and neighbors even if they are disobedient. Visiting becomes more تأكيد (emphasized/important) if it leads to legitimate benefits, such as offering advice and inviting them to righteousness, or winning their hearts, provided the visitor's faith is secure. Evidence for this is the Prophet's (peace be upon him) visit to his uncle Abu Talib and to the Jews.

Thirdly: It is preferable to refrain from visiting if the greater legitimate benefit lies in doing so, such as averting harm to one's faith, or boycotting them in the hope that it will deter them from sins. The act of boycotting varies depending on the boycotters, their strength, and their weakness, and its purpose is to deter and discipline the boycotted person.