From what you have shared your lawyer is trying to tell you that the judge will look at the welfare of your children and given that your children are living at home with you and that you are working hard to maintain your home and have been paying most of the bills, the court is not going to allow your wife to change that.
In many ways you have already won because your wife chose to leave the home and she has been seeing other people and the children have expressed not feeling safe with her because of her abuse of alcohol. You don’t engage in any of these acts and your children feel safe with you. A judge will see that.
Your focus needs to stay on maintaining a safe home environment for your children and maintaining the finances to do so.
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