Should I keep this Tenant? Need your advice

[Jenny Kuria]

I need your advice regarding this tenant.
Her lease began on the 1st of this month but I allowed her to move in on the 28th of last month since the unit was vacant.The background,rental and work verification was perfect. She paid her deposit and agreed to pay her rent portion (she's section 8 )on the 1st. She called on the 1st and said that she broke a window while putting her bed together and needed the window fixed. I told her she had to fix the glass since she broke it. She said that she does not have the money to fix the window and if we won't fix it she will move out.The window was not opening all the way and I had promised to replace it soon. I didn't want to argue with her and I bonded up the window awaiting to put a new one. On the 3rd called to say that the AC is not working. I went there to check on the AC and when I asked her for rent, she said she does not have any money and she'll pay on the 9th. I told her that she should pay or move out by the if rent is not paid by the 5th.Today she said she'll move out on 06/11/11. I wrote a note to her confirming her words and called section 8 to let them know.Then she found out this afternoon that section 8 will kick her out of the program for one year and now she and her mother have been calling me non stop begging me to let her stay.(She just divorced and going through issues according to the mother)
She has left v/ms promising pay the rent on the 9th and that the situation will not happen again.I don't feel comfortable with her and need her out asap but l also want to do the right thing legally.
What should I do??