Prospective tenant conceals emotional support animal

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Hi All: I am a new landlord in Alameda, CA. One of my units in a duplex, we had a couple come in, and tell us: "we know your ad said one small pet is negotiable, but we have one dog that is 50-65 lbs. Would you still be willing to lease to us?" After some back and forth, we decided to make another appointment to meet the dog to see if we were comfortable. Turned out the dog was an angel, and we felt okay about having the couple and their one dog in the one-bedroom apartment. We were still a bit wary of the big dog being in a small space that we had just renovated and refinished the floors on, but they seemed like a nice enough couple. I sent them the contracts for the place after screening them, and after they stated on their application they had one "animal"--not "pet." After reviewing the applications (and this is probably day 3 of holding the apartment for them because they said they wanted it and then it took another day and a half to turn in their application), she contacted me and said she wanted the rent prorated (I said I had no problem with that) but also that she wanted me to redraft the contracts because "[she] has an emotional support animal. And that animal is not [previously disclosed dog." She didn't even tell me what species or breed it was, poundage, etc. She said she had a doctor's letter verifying her need, and that we could not say no under ESA law. I am an attorney, and I also have an ESA. So I was familiar with this stuff. Needless to say we felt very manipulated by this couple who we went out of our way to meet with twice and had discussed this one 60 lb dog at length already. I asked her to please provide the letter before I sent over the redrafted contracts. Another day passes. Then she sends me an expired ESA letter from her psychiatrist. The letter otherwise looks legitimate, other than the fact that it is at least 5 months expired. I told her that the letter was expired and that I would need an updated letter. She said it was "on the way." Day 5 I told her that we would redraft the contracts but had rethought the situation with the original, non-ESA dog, and that we were asking for $70/month in pet rent. She stated that should had no problem paying pet rent for her non-ESA dog, but not for her ESA dog. I again reiterated the pet rent would be for the original non-ESA dog. Her boyfriend then sent me an email stating that they felt I had asked for pet rent in retaliation against his girlfriend for having a disability. He also said they had done everything they could to give me documentation for her ESA, but her doctor was "out of town for a few days," but was gracious enough to send them an updated ESA letter that was "pending signature." As in--a second invalid ESA letter (in my opinion). He then ended his email by saying they did not want to move forward with the apartment and they felt discriminated against and were thinking of filing an HUD complaint. In my opinion--I don't think they have a leg to stand on because the second dog was not legally an ESA (and probably still is not) when they applied for the unit given that the letter was expired. Just wondering what some more experienced landlord opinions are? Another related question is--when you are a prospective LL to a tenant and you say we'd like to offer you the apartment, and then you spend several days waiting for ESA documentation, how long are you actually reasonably supposed to hold the apartment for them before you just go with another tenant? Thanks in advance! Truly appreciate your input.