Wow. What a story. First of all, people usually do train/treat their pets the way they treat their children. She is unacceptable on both counts. In my opinion, it is NOT ok to say nothing. That is how children/women die of abuse. "It's not my problem" is the easiest approach. But as caring compassionate people who want the best for our children/world/earth we need to speak up about behaviors that are unacceptable.

That being said, the how is always the hardest. There are lots of possible approaches. You need to pick one that you're comfortable with. You can even start with "Hey, I've owned tons of dogs and am great at training. Let me show you how" Then, while training explain how hitting is destructive. Then you can gently mention how kids and pets learn the same way. Depending on your friendship and her motivations, she could really learn new parenting techniques from you.
You can enlist the help of clergy or school counselors as singletrack suggested. In the USA you can make an anonymous (but specific) tip to the child abuse hotline in your area. You can simply point out that the American Academy of Pediatrics recommends avoiding corporal punishment. And so on and so on.
Protect yourself emotionally. If she is just frazzled she may be thrilled with your help. If she is just uneducated, again she will be thrilled to learn something new and better. If she is just mean, you and the authorities need to know it.
Good Luck!!