Afraid of teeth chipping or falling out during tartar removal. should i tell her to go easy?

Of course: The hygienist and every health care professional will always try to make your dental appointment as easy on you as possible. Please always communicate to them your fears and concerns so they will be addressed accordingly.

No: Your dental hygienist does not want to cause damage to your teeth, so he or she will be cautious. However, if they have warned you about these problems, that means that you have some serious dental disease going on. Teeth that would fall out during a dental cleaning have advanced periodontal disease and likely won't last very long anyway. Spend some time talking with your dentist.