I advised my children not to accept apples from old ladies ~ they got the point.
But in serious mode The name calling by an ex and telling a child things like this is typical of the "woman scorned". She may not have been scorned but she feels now that she has as she can't abide the thought that her ex's new partner is getting on well with her child. It is fear that is the root of her problem together with whipping herself into a frenzy of unwarranted jealousy. She is no doubt telling anyone who will listen how easy it is for the "new" gf to buy her daughter's affection at the weekends but how she (the REAL mother) has all the hassle of snotty noses, washing & ironing, waking up in the night, taking the child to and from school etc etc etc AND ALL ON A LIMITED INCOME because her bloody father would rather spend his money on some floozy without encumbrances ................. and so it will go on.
The only person to deal with this is the father ~ not his new partner ..... whether your friend likes it or not. By making direct contact and having a go at the mother she will make matters far worse and ultimately it may well cost her the relationship.