People are stressed whether from trying to deal with each other, a baby, or the economy. I am not blaming the OP but you let people transfer their problems onto you. Reading your post I thought these people were unhappy long before you showed up. When you resisted, they turned and focused their unhappiness on you, and worse, the Bickersons then united against you. You were concentrating on your work and did not read them.
There is no reason to think this won't happen again because people are not going to get happier. It could be over anything. The next one will have a baby which they need to go wake up. It's the economy. Or a bad marriage. And you walked into it just minding your own business. Being tuned to people is not just for apparently dangerous situations.
Babies do not need to be put to sleep. They put themselves to sleep unless the household is a tension convention. People use "The Baby" as an expression of their own needs. So I think you wandered into an unhappy place with unhappy people. And soon everyone was unhappy, from them, through you, and right back to the client. (And now we are fighting here but we love that!) Maybe a little mercy despite their unpleasantness, or just keeping your own balance, would have allowed you to get in and get out, with the info you need.