If your stepson actually has a proper assistance dog ('therapy' dogs don't have any legal recognition in the UK, neither do 'emotional support' dogs etc) then the organisation/charity who trained the dog should have explored the family situation before agreeing to supply the dog. If the dog wasn't going to be welcomed in one of his parents' homes, they would have said no.
So legally it's likely to just be a pet, and you can hold your ground on that if you want to.
Even with real assistance dogs (ADs), there's no right of access to somebody else's private home. My daughter has a charity-trained AD and, although this means her dog can accompany her into public places that don't normally allow dogs, it doesn't mean she can expect to take the dog literally anywhere she likes. We have friends and family who have cats, and wouldn't dream of taking the dog to their home unless expressly invited to.
And this is a dog who was selected for the assistance dog programme because of a super calm temperament, she largely ignores our own cats and certainly doesn't bark at them, or chase them, or try to steal their food.
@Sally20099 tell your friend that, although you previously didn't mind the dog coming round, the cats are no longer coping and advice from the vet is that they should be protected from any and all dogs in their home environment. Therefore, sadly, you can no longer have her dog in the house. If the friend takes the hump at this, she is not really your friend.