Question from the service industry

I work at a bar and while we obviously allow service animals, there are quite a few tourists who bring obviously non-service dogs (like just this last week we had a mini-poodle that could not sit still or stop barking at other guests, this was not alerting, and at one point it escaped and tried to run behind the bar)

Would it be acceptable to ask "Is that an emotional support animal?" To someone with a dog that is misbehaving? Emotional support dogs are not covered by the ADA and we would be able to ask them to leave, and someone with a service dog that performs a task (and the dog just might be having a bad day) would be able to say otherwise. I have a few regulars who do bring their service animals, and I want the space to be safe for them.