Honestly, I'd for the most part leave it be. You can't drop hints at them about what might happen. They know what you mean, and they are choosing to ignore you, which in turn is causing tension for all of you. Left un-dealt with it will only get worse. I would think that "allergies" might be a hard sell because he knows you have dogs of your own, even if it is a real issue.
If you have a specific issue with the dog, wait until he is in a good mood - soon - and bring the issue up along with possible remedies. Niece not bringing in the dog is not going to be a remedy that works for them, I imagine. Perhaps limits to where the puppy can be at certain times, keeping it groomed and up to date on flea treatments, obedience lessons, etc.
If you would enjoy bringing one of your dogs to the office, perhaps you might want to suggest a "bring your dog to work Fridays". husband interviewed for a job that had that, and it was a huge plus to interviewees. We were really disappointed that he didn't get that one.
