It’s okay to fire someone, as long as you’re not motivated by an illegal reason. Don’t feel bad for the poor employee who has’t worked out.
There is nothing wrong with employees dating. Nothing good, however, comes from a boss having relations with a subordinate employee, especially one who is a direct report.
If you believe that an employee is abusing FMLA leave, build your case. Uncover enough facts to support your belief that that employee is committing fraud.