My says she is not in love with me anymore how do I ask her to leave without jeperdizing lossing the kids and house?

We have 2 kids and I found out that she has been texting a man for months. I told her that we could work on it and we should go to counseling, but she hasn't to stop the texting. The texting hasn't stopped. I confronted her with it and she just states that it is over and as long as we are cordial that she will stay. I am not good with that scenario I need her to stop texting or to leave because this isn't working for me. When I discuss the fact with her that I need her to stop or leave how do I word it so I don't jeopardize losing my kids or the house?