Wife in love with someone she hasn't met.

Hello, I am looking for advice on what to do. Me and my wife have been married for 4 years and been together for 6, I am 28 she is 27, the other man is 20, we have 3 beautiful children together 6, 5 and 1 the eldest is my stepson from her previous relationship. Me and my wife met online. This first happened 2 and a half years ago where i caught my wife having dirty chats with him. The other man knew about her being married to me and us having kids because i used to talk to him too before all this started. She had left her Skype on her phone logged in so i found everything out and we had a bit of a problem where she agreed that it was her fault and we decided to try again.. Recently she started talking to him again about 3/4 months ago and i didn't think much of it but i went away for a week to visit my parents and when i came back i found that she was talking to him everyday/every night while i had been away. I confronted her and said this has to stop and if you don't i am going to leave (thinking she would choose me over him). She kept saying she cant stop talking to him and i kept telling her if she wants us to work she needs to stop talking to him. Eventually she must have told the other man on the internet and he decided to delete her because he could see stuff was getting real. So we was fine for the past 3 days he had been off contact with her. Today i woke up to find that she was talking to him again. I got angry and told her to choose who she wants and she said "this is never gonna work, way to much damage has been done to fix us." I asked her what she meant but kept saying we are not gonna work. We spoke about 10 mins and she said she wants to split up and took her ring off. I refused to accept it and told her i am not leaving the house or splitting up with her, i asked her if she wants to try again, she keeps saying don't know and wont give me a definite answer. I told her till she meets the other guy and its real i am not doing anything because i am not giving up on us so easy. Every time we argue is because of him and she can't stop talking to him. I know the right thing for me to do would be to leave her, but i love her too much and i don't want the kids to not grow up without a dad (or call him dad if he does come over from Italy) and to top it off my contract with work just ended last week and not really financially good. We own our house, where do i stand if we have a divorce. What should i do? What happens to the kids?

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