Separation from wife living at parents house with me

Hello I have been married for past 8 yrs with 2 kids. We live at my parents house. However, the relationship of my wife is very poor with me and my mother. She is extremely quarrelsome and is also into multiple extramarital affairs (though she acknowledges only one and says it is only romantic and not physical). Our conjugal relationship is almost zero. She says she is ready for a mutual consent divorce. At the same time, she is not vacating our house. She is a housewife and is currently pursuing MA. I used to work outside my hometown but due to the extreme chaos at home I had to quit my job. I now wish to start my life afresh. I also wish to take custody of our kids (aged 7 & 5). Under the above mentioned circumstances, what is the legal way forward? Can I apply for divorce even when we are living in the same house? If I need to evict her first then what is the legal way? How expensive and time taking would the legal procedure be? Thanks a lot.