A: Hitting, kicking, and spitting are not just "behaviors"--they are signs that a child is overwhelmed with anger. A child who has been abused may act this way with everyone, but a loving happy child does not do these things without a good reason. I am not implying that the new daycare worker is abusing your son, but she may not have the skills or the personality to help your son contain his anger constructively or redirect his activities in a healthy way.
Any child will hit, kick, and spit if he is in the wrong kind of situation--and he may bring these behaviors to new situations that are unrelated to the original one. Since your son does not show these behaviors elsewhere, I suggest that you carefully consider whether his daycare is now the wrong situation for him. Can you take a morning off to observe what happens in the daycare? Are there alternative child care arrangements you might try? Many 3-year-olds can be quite articulate, so try asking your son to explain what the daycare teacher and classroom is like and what happens there.