Now if she has not paid yet, that is a completely different animal.

The appraisal was last week and the appraiser said the smell was so bad from the animals and the way the tenants live that he couldn't even give me an immediate accurate number!

With my very first tenant from Hell, the property was left vermin infested with dead animals throughout the apartment.

The baseboards were chewed up from animals so I replaced all of the wood trim throughout the house.

Be sure to evaluate if there are any exclusions that will impact the Liability (pollution, animals, etc.). 

I am in the process of the pre-approval for my 203k loan at the moment but to make things smoother I need to find contractors as well because I am looking into rehab in Los Angeles.

The risk still exists and you need to mitigate it.I would allow him to keep the dog as long as he paid the deposit and then submitted to an inspection to verify the animal was removed and there was no damage.

On the options to keep getting more property, possibly take this year as a learning experience on being a landlord etc and getting your kinks and business in order so you Hebe smoother waters.

Can you show any damage was done by the animals to keep the animal deposit?

The urine smell, it is possible there were previous animals there.