This is just my opinion... I know your sister loves her kids very much and I know you do too as their aunt. I only know what you have wrote and even if their father is a liar and bad man, he's their father. I think your sister just continues to be mom to her children. She has to set up her rules of the house and the actions for not obeying them. She cannot change her ways because their dad is lying to them and making them believe things that aren't true. She needs to sit down with her boys and talk to them. Let them know she loves them very much but she no longer feels she can be married to their dad. She cannot say anything bad about him, they will come to their own conclusion. She has to always be honest with them, let them know her plans, her rules of the house. She may lose her boys for a short time to live with their dad. I think she should tell the boys, hey I will give you one chance, you can live with your dad and if you want to move back with me, then you may do that one time. There will be no coming back and forth. My rules will not change, I will not lie to you to keep you, I will always be your mother no matter where you live, that means I will love you unconditionally.
I think your nephews are just hurting very bad. No matter how you feel about your BIL, that's their daddy and your sister is their mommy. Children are wired to love both parents. Just as parents are wired to love their children (well most parents are). This time is going to be hard on your sister but she will be strong and you are there for her. Don't say anything negative about their dad. Focus on them, on your love for them. Don't change the rules or bend them to make them happy. They will be better and happier in the end if you keep strong boundaries for them. They still need guidance with love.
Hugs going out to all, God will make a way for your sister!
