What can I do about a disgruntled caregiver who continues to harass my family after we terminated her services?

My Uncle, my cousin, and I all take turns caring for my grandmother who has Dementia. We decided to hire a part-time caregiver to take some of the stress off us, as we all have our own jobs and families to raise and take care of. We liked her when we hired her but her quality of care turned out to be very poor. After just a few months she started refusing to take care of the household chores, ie, changing soiled sheets and mopping urin up when there was an accident, are just 2 things amoung many. So after trying to discuss these things with her and pointing things out, she started getting worse, not bothering to wipe my grandmother after she had a bowel movement, and not complying with our requests. After my family gathered to discuss the situation, we decided to let her know that we would no longer be needing her services. She flew off the handle sending emails out saying ugly lies about my family and sending harassing texts to my uncle. I sent her back an email trying to explain our position and that it is final. Now she is continuing with nasty hatefull emails again. I am wondering if we should just block her emails from coming or if there is any legal action we should take to make sure this harassment doesn't escalate?