I would ask your DH the following in a very calm manner: Maybe write it down, get him to reply in pen. sometimes seeing something on paper helps it make more sense.
It sounds like your DH is afraid or ashamed to go against the grain of what his mother says (much like my DH was)
Do you feel the way we discipline our child works for us? Why?
Have we ever resorted to threats and physical violence? Why not?
Do you feel the way my mother treated me with phsyical harm was fair, or justified in any way?
do you feel you deserved physical punishments from your mother as a child? Do you feel they were always justified? or do you feel issues could have been resolved in a more loving way? why?
do you now feel that it would be acceptable for you to hit our child in future? would it be acceptable for me to hit our child? if so-which areas of the face or body would you find it acceptable to hit our child and why?
how do you think our child feels about their grandmother now this has happened? How do you think our child felt in that moment? how do you think our child felt about us as parents and protectors in that moment?
How do you think physical discipline affects a child emotionally?
how do you feel about knowing your mother is likely to repeatedly hit our daughter if in contact with her??
How would you feel if the person carrying out this act was a member of my family or a friend? How would you react?
What do you think as responsible parents should happen now?
Then I would assess the answers given, come to the conclusion that he has said that this either IS or ISN'T acceptable, and then lay out your expectations in full from that point.
He needs to understand that he cannot be "stuck in the middle" here. this is not You V his MOM. this is his mom V his 4 year old CHILD. V HIM. V YOU. there is no middle. Your family unit MUST be his priority.
she then needs to hear what you have decided from HIM.
(As a side note you told her before that if anything like this ever happened she'd not be in contact with your child. she was warned!!!!)
My MIL was cut off by my DH after years of him making excuses for her, until he started to see for himself that she had always been a narcissist, he was afraid of doing anything other than keeping her happy/off his case, that she was behaving in an extremely toxic manner towards our child, and that his marriage was under threat if he did nothing. I stopped her contact with our son, she turned on me and tried to get my husband to divorce me and eventually after alot of outward blame towards me shrouded in the shame of being a disloyal son, he put his chosen family first and 2 years NC we are happier than ever. obv NC is not for everyone but YOUR rules cannot be undermined. this isn't a case of grandma gives the kids kinder eggs and we'd rather she didn't, this is Physical Harm!
Its a VERY difficult situation you are in with your DH, one that can tear your relationship apart and very nearly did ours, but ultimately, your Child and their emotional wellbeing, their trust in you to keep them safe ALWAYS has to come first.
Good Luck xx