Yes, as you exit the elevators the adults only lounge is to the left and the other is to the right. From my limited experience they do enforce that. There are a couple of computers in the adult only side and I wanted to print a few things and I was very politely told I couldn't take my infant in with me. The staff did offer to print whatever I needed and I sent them a few things by email that they promptly printed.

Even in the non-adults only side, I have never found it loud or chaotic (that is obviously very subjective), but the other side is certainly quieter.