If an employee loses composure and respect when given contructive criticism, can I fire her?

Whether given a reprimand or constuctive criticism, this employee becomes verbally abusive towards me, and I own the company. She threathens that she will report me to regulatory boards and have me shut down. She has called me names and ultimately has created a hostile work environment for me. She finally suggested she has a possible mental disorder and has gone a medical leave "until further notice" according to the doctor's note. During her tyrade's she has challenged me to fire her. Can I? I wrote her a letter regarding her behavior and had a performance review completed, but she went on her indefinate leave before tey could be given to her. I have had to hire to fill her position. Don't know what to do with her now, but dont think she is stable enough to work with children. Can I fire her? Will I have to pay unemployment? Is it worth it to have her not ruining my ideal job I built from the bottom up? At this point she has proven herself over paid and completely incapable to do her job.