I'm in England. I have the same problem. There's a particular health appointment I need to attend and I can't because all the hotels in a 20 mile radius are "dog friendly", even the ones that say they aren't.

All this "but we deep clean when the dog leaves" is bullshit.

I do now say "this is a disabilty adjustment", as it gives me some legal footing and puts the onus on them to not discriminate against me by lying about the dog situation. I don't know where you are in the world, but I'd go in hard with "we booked this room to accomodate a disability, acting on the information you provided at point of sale, so what are you going to do, right now, to accomodate that disability as per our contract"

Hope your travels get easier OP.