Your wife must be the one at home with your kids for her to act so RELIEVED, not happy but relieved, at not having to deal with a violent child. My sister has a son who is violent. When he was 9 years old her & my niece used to sleep inside my sisters room with the door locked. When he was taken to get help she smiled but not because she was happy to be rid of him but because she was happy he would be getting some help. Yes I think you have a fml just not what you think it is. Your fml should read “today I realized that my wife was overwhelmed with things with our kids when our violent 9 year old was taken away & she smiled in relief... fml”....... because clearly you missed something wrong that was going on in your household.

Look, it's rare but children can be abusive. You've seen how violent and angry your kid was, enough that you're not arguing that she shouldn't be there. But what about what you haven't seen? What she's done to your wife when you weren't around? It's still abuse, and some abused people experience joy and relief when they escape their abuser. But imagine you had to take care of your abuser or be seen as a terrible person and parent? That's a painful experience. I do hope all of you are able to get whatever care is needed and that your daughter changes and can come back and y'all be a happy family, but try not to hold it against your wife unless you start seeing some more concerning behaviors Kay?

My aunt was a SAHM, the snapping point where her eldest was removed is when they caught him standing over the baby's crib with a knife. If your wife stayed at home with her, I can honestly say having family that's gone through it, she was probably at her end of the behavior and snapped, and couldn't help but feel joyful. I don't know what happened in your situation obviously, but there are many explanations, I could only offer from personal experience.

Dude your wife could be like haha show out now bc you don’t get your way. See where it’s gotten you blah blah kinda thing. Plus kids are violent as hell these days. Not get what they want they start hitting throwing cussing an all.

Your wife's probably the one whose had to deal with this kid for years while you stood around crying.