So we seem ready to assume that the original applicant was being dishonest, and you were played.

You reveal yourself as both dishonest and weak right off the bat.

That being said, since they were dishonest about what the breed was, you should be able to tell them they have to remove the dog or you will evict.

Initially, I wanted to take 1 cat only, no dogs, to minimize the risk of property damages, but now I'm thinking of expanding my criteria to get the vacancy  filled. 

The fact that we live in a society where you can make an investment, be overrun by non paying tenants, swindled by a dishonest seller, and have almost no recourse is the real issue. 

But a dishonest person trying to screw someone over would make sure they created partnerships with as many uninformed investors as they possibly could.

On the other hand, begging for them to bring in the price at a certain number is, of course, very dishonest and immoral.

When an investor says they want to look at a home the real estate agent should say to come to my office, and then the real estate agent gets to copy the investors drivers license and then write down their car license plate number because you have a lot of dishonest investors out there and only a dishonest investor will not provide their ID and then if the investor wants to make an offer the real estate should ask for a bank statement and verify it with the bank to see if it is real honest investors will provide it, and this will weed out a lot of lookers wasting the realtor's time.Joe Gore

That doesn't make them dishonest but it's how they keep their doors open for the services they provide. 

They were not dishonest, in fact one of the things I really appreciated about them in how candid they were.