A. How's a 3-year-old to understand that her affections might not always seem endearing to an eight-pound newborn? Mommy and Daddy always liked her climbing all over them, kneeing groins, chests, and stomachs while delivering sticky kisses. Why shouldn't the baby?
Just as your infant has a lot to learn, so does your older child. She's never been a big sister, has never lived with a baby, and has no context for understanding why her sister should be treated more gently than, say, her dolls. Fortunately, love is the driving force here -- if it was anything more sinister, you'd know it. (A woman I worked with sensed she had the darker side of sibling rivalry on her hands when her elder son repeatedly asked what his baby brother would look like if he was cut open.) Your problem is a relatively sunny one, but yes, do be vigilant.
One way to help both of your girls is to enlist your 3-year-old's support of baby safety rules. This worked like a charm with my eldest, Madeline, when she became a big sister to Ellie. Preschoolers are naturally bossy and love to impose rules on others. Tell her you need her to teach other people how to pat the baby softly. Explain the virtues of the infant seat, how it keeps a baby upright and in a safe place, where her big sister can "read" and sing to her. (Only you need to know that fastening the baby in a padded seat means her sister won't be able to get her in a WrestleMania hold.)
Have her do some nice things with the baby as well, like peekaboo and patty-cake. Let her fetch clean diapers and (with you nearby) hold the baby over her knees for burping, a task both hilarious and gratifying to a big sister. She just wants to have physical contact with her baby -- this is her baby too -- and be part of the action. And right now, the baby's where the action is.