Your options are to sue for divorce. If you believe that your wife's lover, or the manner in which they behave, is a danger to your children, you might include in that divorce a request for custody, or you might (without a divorce) file an action to try and get custody.
Neither Arizona nor Florida will allow you to sue for "alienation of affections," based on the other man's destruction of your marriage (if that's the case; if she left you before she started up with him, even if you had this type of lawsuit available, it wouldn't work). It's an outmoded sort of lawsuit, that dates from an era when women were considered more or less the property of their husbands.
If this isn't affecting the children, now, and there isn't a lot in the way of marital property, I'd consider simply getting the divorce based on the separation or her desertion. These cases are difficult enough at best, without the additional proof elements and emotional intensity that pleading adultery would bring into the matter.
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