intermingling/desegregation

Assalamualaykum Im new to this site, and im not too sure how to use it well so please forgive me if i make any mistakes. I have recently started to become more practising in my deen and unfortunately my parents have not understood my change, i come from a family of very western thinkers and they do not why i have to cover. I have tried to explain to them with patience that as a muslim women i should be covering and i have even tried to explain that this is what Allah commands us to do in the quraan in several places, however they have recently also tried to make out that intermingling and talking to men is acceptable and there is nothing wrong with it. I have tried very hard to explain that we as muslims should abide by the laws of segregation, but i have had some difficulty..i was just wondering if you could help me explain to them or if you could give me any hadith or quraanic quotes that can back my arguement up..i would really appreciate it and inshAllah maybe they can understand where im coming from..or more importantly what Allah has commanded us to do. JazakAllah khair for any replies. Fi amanillah Your sister in Islam