What specialized therapy does the dog do? Does he truly provide some sort of service or emotional support or are they just saying it is a "therapy dog" so they can take the dog everywhere? Would it just be for a visit, or for a long stay?

Therapy pet or not, no animals in your house, period.

Pets are great therapy for, well, everybody who has and loves them, but that doesn't mean everybody can take their pet everywhere they go.

This crap is getting way out of hand. Anything that people can use as a crutch, they do. What is his issue that he needs a therapy pet? He can't come to your home without his pet? I don't think they were ever meant to go EVERYWHERE with the human. Service pets, yes, therapy pets, no. There is a difference.

Sounds like he needs therapy to work on going places without his therapy pet.

Stand your ground.

Your SD might want to do more research on exactly what a "therapy pet" is and does. A true therapy pet is one who accompanies the owner/handler into places such as hospitals, nursing homes, and schools to provide psychological and physiological comfort to others. They are pets first, and and are not granted any type of special access beyond which they have been invited. 

Service dog, yes.

Therapy pet, ? What kind if pet? I recall someone being upset that they would not let the therapy peacock on the plane. Is this a certified trained therapy pet, or a pet that has a printed off the internet certificate? I'd have to see more before I could make a decision, but from the information provided my answer would be no.

If one of you had a severe allergy to dog dander, would you put your health at risk and allow the pet onto your home? NO, you would NOT. You would make arrangements to meet them outside of your home. It's your house.

Your house, your rules. 

A few things. 1-There is a service dog which is for special function of the person, they are accepted anywhere the public can go-and it's not something I would ever deny anyone visiting me.

2- There is an emotional support dog- some places will make accommodations for those, but not always and they can't go everywhere a service dog can.  It's definitely more bullshity and almost anyone can get a certificate with a Dr that writes them a note-airlines are no longer accepting these pets btw...only true service animals.  Emotional support dogs are also not trained pet.

3- A therapy dog is a dog that goes through certain training and goes to certain locations to offer support and a form of therapy for patients.  You will seem them sometimes at psychiatric/rehab facilities, nursing homes, children hospital centers or therapeutic type locations.  They are used for others and not yourself.  

So first figure out what kind of dog/function it is-again, if it's a service dog then I would accommodate.  Then again I never understand prickly/finicky/non-animal people, I simply cannot relate to why/how they are. Like at all.   If your DH thinks his disdain of a little dog hair for a few hours is worth the relationship with his daughter, then it is what it is.  Not a choice I would make personally.   It also depends on distance.  Do they live locally?  No reason doggo can't stay at their home for a few hours-especially if it's just an emotional support dog.  If they are travelling from out of state, it's a little trickier, they can't really leave the dog at a hotel for example.  A lot of people don't like leaving their dogs at home when travelling.  Again, not sure which of these situations you or they are in.  But even for non owning dog people, having a dog over a couple hours once in a while shouldn't ever be that big of a deal, especially if it's your own daughter (and her husband).  Just ask them to clean up any poo outside and keep it off furniture. They can even vacuum before leaving.  But to be so anal as to not allow a pet to even enter your home a few hours, I'd say there's some issues there that go beyond the dog not being allowed, perhaps it's just an excuse to not have them over? I don't know.

Is the SD and her spouse staying with you? Or just stopping by for a visit?
What is the nature of the therapy animal? Some people do need the animal there 24/7 because it can alert the person if they are getting ready to have an episode of some sort.
More information would be needed to give you an honest opinion.