Under the "at will" employment doctrine, you can fire any employee for a good reason like insubordination. It does not make a difference what gender or color they are.
In fact, you can fire her for no reason at all. You are free to fire her just because you don't like her. There is no law against it.
You cannot fire a person BECAUSE of their race, gender, religion, age or disability. You cannot fire a person in retaliation for a lawful act, like taking FMLA time or whistle blowing.
But here, you are free to let her go. The only issue is whether she will be able to collect unemployment benefits. If she was fired for cause, she can't. If she was fired for no reason, she can.
As for how you should handle it, based on what you have said, she is combative and confrontational by nature... so you should probably not engage in a discussion or argument with her. Just take her aside at the end of the day, and tell her "I am sorry, I am letting you go." You can tell her why if you want to, but you don't have to. If you are worried that she will make false accusations, I would have at least one other person in the room while you do it.