Why did Kay leave the children in the unholy and evil environment?

Sure thing Kay is not stupid Kay was leaving no matter what

It seems to me, Kay wanted out of her 'abortion' of a marriage at any cost even without her children, just abandoning them with the unholy and evil father - what a selfish hypocrite!

And Michael was sprung by Kay in front of Rocco! Fancy telling Michael that “children are outside, we are going” in front of a buttonman!
Michael at least had the decency and sensitivity to send Neri and Rocco out of the Desert Inn room before discussing Fredo with Tom

Kay: “The children are outside we're going” “I brought the children to say goodbye to you”
Michael: Goodbye! [yeah, right!]

Tom: That plane goes to New Hampshire
Michael: That's where I want it met!

How can Kay as a mother leave their children [according to Kay] especially Anthony who is 'not' fine, in the unholy and evil Sicilian thing, with the father who is 'blind' to everything other than business and the children's friends are Michael's buttonmen?

How did Kay get the kids?
I doubt Kay got the kids back quickly
Several years is not many The children, Anthony and Mary were little, young at Hotel Washington scene and all grown up in Godfather 3

I believe, Kay's excuse to want out of their 'abortion' of a marriage is unconvincingly lame and pathetic
Kay was happy to enjoy the spoils of the unholy and evil Sicilian thing for five years, the 'original' time frame for legitimacy and then two more! Go figure!

Nevertheless once Kay got into Michael's car at New Hampshire....!!