Thanks, all. I had no idea about the first class rules for international. We would have been told at booking, but I'm glad to know ahead of time.
Our dog is so well behaved the other passengers don't eveh know we have a dog until we are deboarding the plane. In fact, the carrier doesn't look like a carrier, so most FAs wouldn't even know it's a dog. We'll just fly under the radar
The backup plan is me staying at home, with the dog, without the company of my inlaws. How upset do you think I'll be?