First off, I'd stop drilling him on the "please and thank you" stuff. He'll learn to do it if that's what his significant adults are doing most of the time. It sounds like maybe he's had the experience of adults refusing to help him 'til they hear the "magic word?"
If that's true, I'd just apoplogize to your son and say you didn't realize that insisting on "please and thank you" might make him feel it was okay to refuse to help someone if they didn't say it "right." And that it's important for us all to help each other, and it hurt Grandma's feelings when he refused to help her.
About the hitting -- I don't want to imply that your mom would be dishonest and say she didn't touch your son if she did. But the way you're describing it, the hitting doesn't make any sense if she just asked your son to open the door, he refused, and then she went ahead and opened it herself (maybe after she had to set her stuff down) and came in.
Why would he just run in the door behind her and start hitting her? It just seems more believable to picture her asking, him telling her something like, "Not 'til you say the magic word!" (or else just quietly waiting for her to say it), and then her opening it herself and angrily dragging him through. And then
him hitting her because he's rightfully enraged at getting manhandled.
I'm not excusing the hitting -- but as an adult if someone tries to drag me through a door, I have a lot more power to stand up for myself and make sure it never happens again. A child in that situation often feels powerless and their anger feels uncontrollable, because they honestly don't have adult resources for handling this sort of disrespect.
I don't know ... you know your mom and son and I don't know them at all. I'd believe my daughters over my mom any day, because my daughters are honest with me while my mom has often been dishonest with me.
So it's really your call who to believe. But just based on a brief analysis of your account of this incident, I'm thinking your son is being more truthful than your mom.