Feeling bad about hurting other people comes with time even for that of a four year old.... many kids act like your daughter is at this time in their development and it is up to you "the parent" to teach her other wise.... imo some form of disciplinary action needs to take place every time she does some thing that physically hurts another person (even if its just time out in her room) and you should always correct her when she states a negative thought about hurting a person or a dear loved one.

Hang in there.... and remember the old saying "parenting isn't for cowards"
well, is there for a reason.