How to you deal with betrayal, from spouse?

was married for a dozen years + then one day wife does decided that she didn't want to be in a relationship, or felt that she couldnt forgive herself for what she done, (adultery) i dont know but how can a woman just walk away from her children, Im a husband who gave her the world and freedom, working man and raised her child (her past relationship) and another baby that came into our lives. ive asked if she would come home, i would leave until such time we can worked it out if possible and still support them. now i don not want the kids to leave as they are better off with me in the first place since i raised them. how do i deal with the betrayal as its slowly engulfing me with hatred. kids are ok as we always talk and i do tell them to never hate their mother as she will always be their mother but slowly the oldest one is losing that respect for her and doesn't want to hear her name in the house.