Lety, you don't put enough information in your post to get clear answers - why is she objecting to her son having a relationship with her ex?
If there is indeed a deeper reason and specifically if it is fear of abuse, i strongly suggest that she and anyone else interested look up an article named "What Is Fair for the Children of Abusive Men?" by Jack C. Straton PHD. Google Abusive Men Children and you'll find it. And then fight tooth and nail to protect your child.
There has to be a reason as to why she won't let him stay with his dad. If it is just out of spite for them breaking up, I would advise her that the childs father could take legal action to see the him. If there is a deeper reason as to why, she needs to make sure it is taken care of in court to protect her son.