Need advice on an unusual problem

[Howard H.]

I have a single family rental house in St Louis. The tenant has been decent and pays the rent. The tenant advised me that she wants to vacate well in advance of the lease term to move in with her Fiancée at his home after their wedding. I attempted to follow up a few times and get a timeline for her wedding and intended move-out but she would not reveal the information. Several months went by. She continued to pay the rent at the first of the month and never talked again about breaking the lease. I learned just a few days ago that she did move out of the house and is married and living with her husband. She has allowed her 21 year old daughter and the daughter's boyfriend to move in and occupy the house. She did this without telling me and in direct violation of the lease agreement. I found out about this because the kids have turned the place into a party house and I got neighbor complaints and the police have been out to the house. I have spoken with the responding officer and have the police call log. On July 4 they destroyed the garage door and never informed me about it. The lease requires that I be immediately notified if damage occurs. I found out from the neighbors. 

The rent for July is paid. I have spoken with the lessee and she has agreed (via written email) to vacate and have all property out by July 31. I have told her there can be no occupancy without her residing there and then only her and 1 other person per the terms of the lease. However, she will not sign and return a lease amendment agreeing to vacate by the 31st and acknowledging that she must occupy the place or nobody can occupy the place. 

There is an abandonment clause in the lease but that seems to be tied to non-payment. Since she is paid up, I am not sure it applies. 

Any suggestions on how to handle this would be appreciated.