Just wanted to put the disclaimer out there first...
For us - we had the trainer three or four sessions. We could have used more. It was more of teaching/training us, the humans, than the dogs. She taught us ways of dealing with the dogs. It was up to us to enforce & reinforce those rules. If you (and DH) are good about that - then it shouldn't take long.
I didn't see the episode, but I saw that the dogs were taking a liking to DD's toys. Remembering what I learned from the trainer, I made sure to distinguish between DD's toys and the dogs' toys. We haven't had a problem since.
Also - DD's relationship with the dogs have changed since she was born. It's been fun to watch.