K.C.
Her son is acting out because of the turmoil at home. He is angry, sad, and confused and doesn't know how to deal with his emotions. Unfortunately, he is taking it out on your son. It sounded like the mom handled him when she saw him shove your son in the field, and that she didn't see what happened at the dance. So she isn't just letting him get away with whatever he wants to do, as far as I can tell from your post.
Now, for your friend herself... a good friend of mine is in a very similar situation (husband left, nasty divorce that's dragging on forever, suddenly single mom to two young kids). So, if your friend is anything like mine, here's my take on it: she is also angry, sad, and confused. She's going through what is most likely the worst thing she's ever gone through and she is miserable. She's probably scared. She's retreating into herself and cutting off contact with friends for several reasons:
1. She's too miserable to talk to anyone, even about the most benign topics
2. She knows she is a downer right now and doesn't want to bring others down
3. Other people's happiness and normalcy makes her feel even worse (even when nothign is being outright rubbed in her face)
4. She can't think about anything but the divorce and therefore can't talk about anything else, so she's not talking at all
There are so many reasons why she is retreating right now and I don't think any of them have to do with you directly. If you are currently in a happy marriage, it may be hard for her to be around you right now - not because of anything you're saying or doing, but simply because you're happy and she's not.
So, what can you do? Talk to her - not about your son's bullying and not about thinking she's mad at you. Just say that you notice she's been quieter lately and that you're always available to talk if she needs someone, no matter what she wants to talk about. Bring her dinner one night so she doesn't have to think about cooking for her kids. Offer to have her children over so she can have an afternoon to herself. Be a good friend to her, because that's what she needs right now.
My friend retreated for a long time. Our sons had been really close friends, but she didn't have my son over to her house for two full years - for several months before her husband moved out and for 1.5 years after. But, she eventually started talking to me more again and started having my kids over for play dates again (like you, our sons are very close and their younger sisters are very close). She just needed some space because she wasn't up to talking to anyone.