You guys had some close guesses! Here's what the vets have told us for each:
Bailey - Chihuauha x Daschund mix. Funny because I hate Chihuauhas because of their temperment, but I love her to death! You won't find a better lap dog, and she's never offered to nip or gowl at a person.
Conner - Supposively a German Shepherd x Labrador, but I kind of dissagree. He's a bit smaller than I'm used to seeing with lab mixes. No idea what he'd be otherwise though.
Prince - Chow x Labrador or Chow x Golden Retriever. We're 99% sure of chow because of his howling/yodeling and purple tounge, but the other is fair game to any guesser xD