As per usual, MN users all pile on, to tell the Op, that it's abusive, and her son will go NC with her when he's an adult, and that she won't see her grandchildren. 
There is a world of difference, between a hard blow to the face, and a tapped bottom. We have no idea what is happening here, or the frequency.
I have witnessed horrendous behaviour by children, that literally goes unpunished, and I think I might have given a tap to the bottom, or a stern telling off, however, current thinking seems to be that children can set the rules, and must not be challenged. I'm not sure it's working, because I see a lot of kids who are out of control, doing stuff I would never have allowed my own kids to do.
I was repeatedly smacked as a child. Probably from about age 5, right though to 16. And I'm talking proper hard whacks to the face. In fairness, only ever when I was a total shit bag, and yes, I deserved it.
We were also left in the car, with a bottle of pop and packet of crisps, whilst the adults had a drink in the pub. No seat belts in cars. Very little mollycoddling : if the teacher said you'd been naughty, you'd get punishment at home. No fancy pubs with ballpits, you were lucky if the park had a seesaw or a slide.
This was fairly standard for kids being raised in the 60's, 70's and early 80's. We are all still alive. I am not NC with my parents. They love me fiercly, but parenting was different then. They never ever hit my children, as it wasn't their place to parent them.
My own parents childhoods, were far harder than mine.
Not sure what I'm trying to say, but I hate this label of "abusive" that is bandied about so freely on here. Perhaps get the Op to describe what is actually happening, before piling in. I can't get worked up, if it's an occasional tapped bottom, when the child's behaviour is intolerable.