At three years of age, children are still quite ego centric and thus "sharing" is difficult due to developmental issues and not because she is "selfish." At this age, it is best to share time with a toy rather than sharing the toy itself. If a toy is desired by both children, you can limit each child to 10 minutes of play. When the time is up, tell your daughter "Oh I see, it is the baby's turn to use the toy." I would not allow either child to take a toy from the other. Simply intervene and give the toy back to the child who was playing with it first. If there is protest, simply tell the child, "I know it hurts to want a toy that someone else is using, but you may not take the toy from your sister." Children this age are learning proper social behaviors and do not, as yet know the rules and must be reminded of them consistently. It will be some time before your child will just follow proper behaviors on her own--at this point in her life, she needs your guidance and insistence that she follow rules that will eventually become second nature to her. Instead of looking for ways to punish her, just try to view each misbehavior as another opportunity to enforce and practice the appropriate behaviors. Patience, calmness, and consistency is the key.
It is normal for her to be jealous of her baby sibling. You might often point out the activities that a three or four year old can partake in that a baby cannot. It is fine for her to mimic the baby--this is the kind of play that leads to understanding the perspective of the baby and will not be harmful in any sense. You might tell her that you notice and then distract her with more age appropriate activities. For instance, if she is making baby coo sounds, you might say, "Oh I see you are making sounds like the baby makes. I am so happy that you know words and can talk to me." There are many advantages to being almost four! However, children at this young age sometimes regret leaving the safe feeling of being a dependent infant. She still needs to be held and cuddled, at times. She is in a time of transition and therefore, both sets of needs are still present to a degree.
Thank you for your question and if you would like further answers, please respond and I will reply. Thank you again, Dr. Tarey