I want divorce but wife keeps on changing her mind in making the decision

I have been married for 3 years now and have a son who is 2 years old. My wife was having an affair before marriage and she told this to me at the time of our marriage. She said that she has broke up with that guy long back. So i accepted her. Few months after marriage she started quarrelling with my mom on small things. It started increasing day by day. We had a meet with her parents that time she said sorry and gave us in written that she will not misbehave again. Few months went good but again same things started. This time she started lying with us. One day I saw some messages on her phone which shows she is having an extra marital affair. She also talks with that person over phone till the late night. But she is not ready to accept it. I have asked her not to talk with that guy but she don't listen. Instead she tells us different stories every time which are hard to believe and illogical. Later she started making false comments about my parents and said that she want divorce. I want to give her divorce but now she is refusing to sign and asking me to live separate from my parents. She is harassing me and my parents mentally and making false statements. And now she is including my sister's name also in all these false comments. She is a working woman. Please advice me how can I get rid of her. I don't have any property on my name but my dad has. Can she claim on it? Also I want my child custody because I cannot risk his future by giving his custody to the mom who is having an affair and may marry to that person in future.