I'm going to accept your words a face value and assume that your son is in an abusive relationship. The default, male or female, is 'I believe you' so I'm operating under that premise.
He needs to report her assaults, on his person or on his belongings, to the police. And he needs to move home, permanently, regardless of her threats. His access to his child is for the courts to decide. He is too young and too immature at 20 (I assume) to deal with this without support and professional advice. Until the baby is born there is nothing else to be done. He has no rights to be involved in her pregnancy nor to be present at the birth. But reporting and 'building' evidence of her abuse may help him in court access proceedings.
IF she refuses to put him on the BC, 'theoretically' that absolves him legally from having to pay child maintenance (hear me out before flaming, MN!!!) since she is not claiming him as the father. Do you really think she's going to forego financial support? Unless she's from a family who will support her financially, I doubt it. So she either names him on the BC or names him to the CMS to get maintenance. If she names him on the BC (although he must be there at the registration) that establishes parental responsibility. If she names him to CMS, she's 'admitted' paternity and establishing parental responsibility through the courts should be relatively easy. If she does neither then he will need to file his own suit to establish paternity. Following that would be court orders for access to the child AND for him to pay maintenance (as he should) when/if he is able.
No matter which road he ends up taking, a DNA test is in order.
As a grandparent, you have no rights to access. Your access would depend on your son's access. If she refuses to allow you to see the child, your only hope is that your son gains access and you see the child on his time. The rare exception to this is for grandparents who have played a major part in a child's upbringing.