Thanks for spelling "advice" right. 9 out of 10 times this same question is posted as "I need advise"... drives me nuts.
I think first I would talk to the little girl. "Wow, your mommy said/did that? Why do you think she got so mad to say that, what were you doing before Mommy said that?" Maybe you can get some more info to help you when you do decide to approach mom.
Then, I would casually bring it up in conversation: "Liz, Amy seemed a little frustrated last night, she mentioned that you are sending her away to Daddys house, she seemed so upset about it, what happened to make you say that to her?" Sounds like Mom needs someone to vent to and the only people she has to do it with are her kiddos.
Now you may not mention anything to the kids or to the mom at all but REALIZE Mommy has some frustration problems going on and you can now, with that insight, maybe help her by opening up a friendly door so she feels comfortable enough to vent to you...... that alone may take the frustration away enough for her to stop using the kids as her target.
Does she drink? It sounds to me like she might be having a few cocktails at night, alone, gets a littld tipsy and then forgets that she's wearing a mommy hat and blows all of her maternal instincts out the door and starts somewhat abusing the children, alcohol will do that to the best of us on occasion. It's easy to take something small and make it big when you are drinking, and not care who is in the fallout of your alcohol induced rage session.