Eviction Posted On Tenants Door?

I have a new tenant that just moved in and has been there for two weeks only. She has no furniture and has a puppy in there that was not on the contract and a guest (boyfriend) that is keeping his vehicle in the garage and the place is dirty and dishes every where & she has two little boys that are sleeping on the floor. She has destroyed my garage door and I had to put a new one on for $350. She does not have anything on the move In Inventory form that there was anything wrong with it and it was all tore up at the bottom. The only thing I can figure is that is got caught on the boyfriends vehicle because the whole bottom was torn off. She said it was rotted. I went to make a repair on a small hole behind the door and that I when I saw the condition of the place & the unauthorized pet in there & the boyfriend sleeping there. I went home to get my camera and came back and took pictures. She has also left the two & seven year old boy by their selves because it was called to my attention by two repair men that were replacing the garage door & fixing the A/C heater. She filed a Police report on me for harassment. I posted an Eviction Notice on her door and now she is sending me E-Mails requesting her money back and she will leave. Should I go ahead with the formal Eviction? I am in Austin, Texas.
She paid $775 for the two weeks rent and a partial security deposit of $388. Real Estate agent got 80% of the first months rent. The rest was suppose to be paid by March 1, 2010. A total of $2325. First & last months rent and the deposit had to equal the rent.