Seems to me like your doing a little dishonest yourself.

Don't be dishonest.

When I emailed them that I need to do repair service to restore the garden and attached the damaged photos/videos, the husband still claimed he took good care of the garden, and adamantly hinted if I deducted the amount from the deposit, they are going to go through court to sue me...These tenants are so ugly souls who are dishonest, disrespectful, I felt extremely frustrated that I am thinking of selling my property for good to avoid dealing with these terrible terrible people again.

There is plenty of misleading and dishonest information here.

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.