People who make bad decisions attract similar kind and are  usually in specific situations that do not match where they should be at their age.

Are there any suggestions on what needs to be defined in the lease regarding this and suggestions on whether increased monthly charge or an additional "pet deposit" is best for protection of our property?

The bank statement will look at your gross deposits and use  calculation to divide that into a monthly income to pass your DTI requirement. 

@Danny KaminskyAnother factor: Many people with kids, are getting unto $500 per month deposited into their bank account until 2025.      

Once I have who I want I respond through text thank you for your interest however I have just signed a lease with another applicant and taken a deposit, good luck on your search. 

One thing I would say is be nice to the tenants because my guess is you just have maybe a one month deposit and if they get mad they could do more damage than you could repair with their deposit.

And they caused damage to the unit which will most likely exceed their deposit.

It might be helpful to get connected with a buyer's agent who can set up an automated search directly from the MLS (multiple listing service), then you will be notified in real time as soon as a new property that matches your search criteria hits the market. 

Well, we have the deposit to hold and we were to meet and do the walkthrough for the new tenant move in checklist today and finalize everything.

If she was offered more money from another investor/wholesaler, could you beat/match that offer and still keep the contract with her?