Like I said, it's her problem. She's an adult not a "case" you need to fix. You have a duty to the children and to the law to report actual or suspected abuse which you can certainly do anonymously. I'm sure you can make the report 24-7, too, and holidays are stressful, so if more were to happen, this is a very likely time.
I hope you all the luck in the world with this. I also hope your friend sees the need to get on board with you in this fight and your friendship remains intact at the end.
These things are never easy, I have given support to people in similar situations before and I can only hope that the results of your brave effort is positive. Although this isn't always the case, never doubt that you are making the good call on reporting.
if this turns out to be a longer battle, there are ways to help yourself and the child. record everything the child tells you, the date they tell you and when these things happened. try to gather other evidence if possible, have any bruising or marks autographed by of with at least one parents (have to keep yourself safe) or a doctor whom you will want to show the marks. You could also look into the laws of the use of secretly recorded conversation in the court room. If its legal where you are, a criminal will often try to rub your face in it if they think they have you beat, you may be able to play on this. That last one is very dependent nerve, law and how comfortable you are doing something like this.
Again, I really hope this works out, of course for the child sake, but also because what you are doing is a very hard thing that many would ignore for their own convenience.