Is it possible that other children at the scool hit and push if this behavior has recently started it sounds as if it is from there. The Teacher should give him a time out also, perhaps she isnt handling it to well.Ask her what tiggers the hitting ,are they stimulated enough as boredom can make children misbehave? When he is sullen with Granma tell her to interact with him some Games and Fun, she will win him back ,tell her to make an effort there,if he is bad you give him a time out .
I'm sorry to sound a bit rude here, but, really??
Unless your son has an underlying medical condition that is making him difficult to teach manners to or makes him out of control (ie. autisic comes to mind), the only problem you are having is discipline. He has been in school for two weeks and is hitting and pushing??? I am going to make a leap here and assume that the reason that he resents Grandma is because she probably expects him to treat her with respect that is due her.
You need to set clear rules and consequences and follow through. Every time. Whether it's convenient for you or not. If it means you don't eat out for the next six months while he learns table manners, or you can't have a night out because he won't mind his babysitters.
If you cannot get him in hand at 2, what is the possible outcome of his behaviour later on? This is truly the most important job of your life...Stick with it and you will succeed!