The one thing you cannot do is take this matter lightly or ignore it.
You may feel you are being robbed or blackmailed and most likely you are but you cannot let it slide. The deck is stacked against you and you will have to pay something. You should visit the secretaria de trabajo yourself and report the situation and get all your personel files up to date.
From now on, when you fire someone you should call the S.E.T. FIRST and ask them to send an inspector by and ideally fire the worker themselves. (you still owe the worker some money, but not 40 weeks of pay, more like 4-12 weeks depending how long they have worked for you)
Here you can find an online calculator that may help you to determine how much you actually owe your employee:
http://www.set.gov.do/main/calculo.htm
If you do not take immediate action though, the law will take the employee's word for EVERYTHING and charge you whatever the employee is asking for , plus a little more just to rub salt in the wound.
Basically you have already been screwed, so just deal with it as best you can, try to come to terms with your former employee and get them to accept a reasonable settlement. Make yourself aware of all deadlines involved with the case and don't let anything slip or you could find your mission and anything you own "embargado" bank accounts frozen, etc.