11 months old?? Holy cow! That's young for this behavior. At least in my experience it is. If she's throwing a fit when someone comes near her, it's probably because that person does something she doesn't like. Watch how your 7 year old treats her and see if there's something she reacts to (other than her coming near). As far as the hitting and tantrums, it's probably to see what reaction she can get. I think it's because she doesn't like or doesn't want to do whatever is going on (like diaper changing), but she probably does it because it gets her the result she wants. (like stopping the diaper change, or going away, or putting her down when she hits, etc.) At that age, I'm not really sure what to do as a consequence. But maybe try pulling her out of the environment she is acting out in. For example, if she starts throwing a fit because sister is coming near or doing something not inappropriate, but that she doesn't like, pick her up and put her in a playpen or her room or somewhere removed from the situation and tell her to stop crying or "no." She may not understand "stop crying" or even "no" but at least she will begin learning the meaning of the words because she's isolated for her behavior. I think eventually she'll get the point that she's not supposed to react that way. As always, react very positively when she behaves in a way you approve of, and negatively (without yelling or being "scary" to her) when she behaves inappropriately. Good luck. Hopefully it will help. I'm not used to dealing with that behavior in someone so young.