Congrats on the new baby!
But do understand that this is a trigger for 2 and 3 year olds. You left the house for a few days, and you came back with a crying fussy 7 pound creature whom everyone is fussing over! The novelty of this wore off in about 15 minutes, and now your 3 year old is acting out.
You can't ignore screaming, hitting and kicking of Grandma, or of anyone else. You must separate him from the group (or the person) immediately. He goes right into isolation. For a 3 year old, it's for 3 minutes. Do it every time. Don't talk a lot - just "NO! We don't kick." Then into his room. He can go into time out elsewhere if he will stay there, but if the 3 minutes is spent telling him to sit down, then he's getting the attention he seeks. So find a way to isolate him. Then welcome him back to the group. Next infraction: repeat the isolation with the simple "no" statement. It's annoying but don't give up, because it will work.
I disagree with forcing young children to apologize. First of all, they aren't really sorry. They are too young to really have empathy for another person. They only know what affects THEM. I think, at this age, apologies make kids feel that they can do anything they want as long as they say "sorry" to make it all okay. If he continues to scream while in his room and doesn't calm down in the 3 minutes, then you go in and tell him that he's not quiet yet, but when he is, he can come back to the group. Then leave, and wait until he is quieted down.
He may be associating Grandma's daily presence with the whole new baby thing. This is a change in his routine.
He also needs to see Grandma as an authority figure, which means she has to be allowed to put him in his room if you are not there. If you ARE there, then it has to be Mom and Dad who do not tolerate this behavior.
I realize this is hard to do when you are 10 days post partum and completely exhausted. If Dad or Grandma can take the baby now and then so you can spend a little time with the toddler, great. "Isn't it nice of Grandma to come help with the baby so you and I can have some special big boy time together?" might work. But also do as much as you can all together so he understands that this is the new family configuration - say how nice it is to sit and read together, or to snuggle together, etc. You can tell him how much the baby is going to learn from him and enjoy watching him do puzzles or play with blocks or whatever - but it may take a while for that to really be interesting to him. Also start soon with things like cleaning up non-baby-safe toys so that when your newborn is crawling, your 3 year old is already in the habit of keeping things away from the baby.