Do what you think is right. Your kids will eventually learn the truth, and since she's not spending time with them anyways, they'll naturally gravitate towards the parent that gives them the most time, love and attention.
WAW with kids have a huge amount of guilt. It's easy for our pain and anger to forget how hard it is for our spouses. And easy to feel like it's their just desserts. But if we truly love them, we have to be compassionate; compassionate doesn't mean a doormat though.
Focus on your values; choose your actions based on your values, and accept your emotions. Don't switch these around...
