Hey mummy, I think it sounds like a combination between the "terrible 2" stage and the feeling of being replaced by a sibling.
First of all, 2 year olds don't have much concepts over the "proper" way to care for someone else - so all that kissing, hugging and even trying to poke his sister's eyes etc can just be his way of trying to show his affection to his sister! He's also at a stage where he wants to do and explore everything, and do everything on his own - so when people get in the way (like your mum), sometimes we can get hit unintentionally :x
Another thing is the "sibling rivalry". Like what some mummies already shared, having your love and attention for 2 years and then suddenly having all of that "taken away" by his sister may make him feel upset - especially when regular routines like bringing him to school is interrupted. His way of trying to get your attention and love back is probably through the bonding of direct latching with you, and he isn't willing to share it with his sister because he might be trying to make a "statement" that "Mummy is mine!".
What you could probably try to do is to foster the bond between them, it's gonna take some time - but get him used to being around his sister and teaching him the proper ways he can sayang his little sister. You can also get him involved in caring for his little sister, but only if he wants to - make it a fun and happy experience than having him feel like he's doing chores for his little sister!
Other than that, try to set some time to be with him alone too - I know it's hard with a newborn, but simple things like bringing him to school or even just lying down together when his sister is asleep :)
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