Should I evict my tenant?

[Trang Vo]

My tenant is consistently late on rent for the last 3 month. This month is even worse:

6/7- I sent out a 3 day notice to pay or vacate per law. She replied and asked to pay rent and late fees on 6/16 due to emergency. I said No. I let her know that I would file eviction suit on 6/14 if she didn’t pay or vacate. 

6/14- she paid through apartments.com

6/16- payments failed because of insufficient fund. She said something went wrong with the portal. I gave her the benefit of the doubt. I told her it was okay with casher checks. At 0930 PM she dropped of her cashier checks and $400 short. I texted her that I wouldn’t cash the checks and would keep them as evidences for court. I also texted her that  If she moves out by Tuesday 6/20, I will give her checks back, and no eviction will be pursued. If not, eviction suit will be filed. I no longer accept any more payments from her. 

6/18- she dropped off the remaining of the payment at 10:15 PM. 

My questions are

1. Do I have a good eviction case against her? 
2. Will it affect my case if I have the cashier checks in hand but not deposit yet?

Thank you so much for everyone’s input. I really appreciate all your time and help.