The baths are private, not shared. Not sure if kids would enjoy the baths. They last 40 minutes, and it is just you in a deep tub in a quiet, low lit room with light spa music playing in the background.
As for the rooms, the hotel does allow pets. I've been on the elevator with people who have dogs. My husband is very allergic to cats and he doesn't have a problem at this hotel, but then again we usually spend a lot of time outdoors and not in the hotel itself. If your kids are very allergic, even to dogs, then I would consider staying somewhere else. Also the hotel is older and somewhat renovated, but I have never found it to be dirty, or really dusty, but there is carpeting in the rooms, so again, if your kids are very allergic you may want to stay somewhere else.
Not sure when renovations will be complete. I would inform them about your allergy concerns. Customer service has always been good there. I have a dust allergy as well and had no issues there. I've seen pets there not sure what floor(s) they are allowed to stay on