Teaching a 2 Year Old to Stop Hitting & Spitting

My 2 year old son, Greyson, keeps hitting me and the dog. He's also spitting milk on everything and running up to me and spitting. I've tried everything I know to do to stop this behavior.

I've explained that it's not nice to hit and spit, that it hurts Mommy's feelings and makes Mommy sad. I popped him on the hand once when he kept hitting me harder but that just encourages it. We've done timeout where I put him in a chair for 2 min. When he tries to sit up I tell him Not yet and remind him he's in Timeout then explain what happened. He tells me sorry and we hug. My grandma has began pretending to call Santa and saying Greyson was being a bad boy hitting and spitting at mommy and the dog and telling him to be a good boy. It doesn't matter now much I tell him No or to Stop.

I don't know how to teach him that it isn't ok to hit or spit at others, even the dog. Nothing I've tried seems to be working so far. I don't want to yell at him or feel like I'm getting onto him for it all the time and he doesn't understand. Any advice or things you've done that have worked with your children would be greatly appreciated :)