You're treading in dangerous waters. Consult an employment law attorney before taking any action. Spending some money now on an attorney to extricate you from the mess that is developing could save you many thousands of dollars down the road.
What you need to do (actually, what you need to have an employment law attorney do) is conduct an investigation into her allegations before doing anything. Yes, her complaints may be totally bogus - but you can't just assume that. In order to have a legally sustainable response if the complaintant takes this further, you need to be able to demonstrate her allegations were fully investigated and you subsequently took whatever action is appropriate based on the results of the investigation.
If you fire her at this point, she'll immediately bring a claim to the State/EEOC for retaliatory discharge - and that could cost you big-time.
A person, who is nice to you, but rude to a waiter, is not a nice person. (This is very important. Pay attention. It never fails.)