I have a 7 year old DD, so right in the age range you described, and this behavior seems extremely OTT. My child knows not to interrupt when adults are speaking (she has to be reminded some times, but only once) . For this child to shove books in your face repeatedly, step on your feet and grab you and go through your purse during a business meeting is so wrong and unprofessional. I would have told the lady that you would like to reschedule the meeting for another day. If this woman has her DD assist her in many more business meetings, she may find she has no more business. It has nothing to do whether you like kids or not, or know how to relate with them or not, her DD should have been made to sit quietly until mom finished her business transaction.
I have no problem with unruly kids and their inattentive handlers being sent on their way in restaurants. If I am going to spend money to eat out, I don't need the SS family ruining it for me. I do NOT allow my kids to act like heathens in public and I do not appreciate being subjected to others ill behaved kids ruining my dining experience. Call me condescending or a child hater, but there are basic rules of conduct that children should be taught and not being a pest during what is obvious not a child centric business transaction or acting like screaming mimi's in a restaurant are big ones.