Yes, you absolutely have the right to be mad. Your niece is leaving you with a mess and has shown no responsibility for her actions. She is disregarding your feelings and your property. The other issue is that she maintains control and is continuing to string you along until she decides she is done. That would make anyone frustrated and upset.
The main problem here is lack of control. The situation has left you with few choices but to wait out your niece's lease and allow her to have control over the situation. That is difficult.
Although the situation leaves you with little control for now, there are some things you can do to help yourself.
Your idea of having her cover the expenses of the clean up is excellent. There is nothing wrong with you sending her certified letters saying that you will be estimating the cost of clean up and charging her for the expense. That way, you have clear proof that you warned her. Also, take pictures of what she leaves will give you evidence in case she tries to fight it. You may also want to take a witness you trust to back you up.
Consider talking to others about your situation, especially landlords in your area or on line. There are many who have gone through the same situation and can be supportive and helpful to you (I know one personally that had to deal with tenants who left feces in her vents. She was not happy!). Also, contact your attorney to see if there is any other recourse you have and how you can be sure you have covered all the bases in case your niece fights the cleaning bill.
Also, be sure to take care of yourself. Working out your anger and feelings of frustration is important so they do not adversely affect you. After you have done what you can to protect yourself, a good distraction helps. Exercise, time out with friends and family, getting away for a few days and relaxing activities are all examples of how to help you cope with the stress. And remember, this will be over soon so you don't have much longer to wait until you have control over the situation.
Let me know how it works out for you and if I can do anything else to help,