How do you evict a "roommate" for non payment of rent?

My Fiance and I hold the lease our seven bedroom home. For the last two years we have been renting out rooms to fellow college students (The home owner is aware of course) With the verbal understanding that rent is to be paid on the first and an 80$ late fee will be added to any rent paid past the third of the month. The same extends to bills as they are all in our name. Any bill paid past the fifth is subject to a 15$ late fee. I also have the agreement posted in writing in a common area of our home. One of our room mates had been dodging us on rent up until the 5th of the month. When i finally got a hold of her over the phone she informed us that she was going to be moving out on the 15th and would not agree to the rent rate that we quoted her. Since then she has refused to pay us rent,bills,any late fees or her portion of the quarterly water bill we expect to receive next month. She does, however, Intend to live at our house up until the 15th. we intend to go to the courthouse on Monday to obtain a 72 hour eviction notice for non payment of rent, and proceed to small claims court to settle our debt from there. In addition we discovered that she has been gone for three days and shut her cat into the bedroom without food,fresh litter, or water. This morning i entered the room to feed her cat before sending her a text to let her know i had done so... Didn't seem like a big deal to me but now she is threatening to counter sue us for all of her debt because i failed to submit the entry in writing 24 hours in advance....... does that even apply to family's renting out rooms in there own home? What happens when we serve her the notice and she inevitably does not come to get her belongings? I have never had to evict anyone before so im not exactly sure what bases i need to cover. Any help would be greatly appreciated.