Gaiman plays with mythology, but he also plays at mythology. The Endless, like classical Greek gods, descend into petty squabbles that mortals would quickly resolve. Grudges, such as Desire's grudge against Dream, can fester for decades or centuries because time is not a factor.
Night represents darkness, of course, but the darkness can obscure as well as hide. Mothers play favorites, even if they claim otherwise. Before she helps Morpheus, she wants to pinch him, and not in a good way. She mentions the other children. He brings up Desire, but before he can ask for information or intercession, Night pushes one of his buttons. He whines. The moment passes.
My conclusion is that Night is playing with Dream. She claims that Desire doesn't visit, but she knows about the plot to destroy Dream. Before she can give away anything, she distracts him and changes the subject. She knows Desire and Dream are not alike. After all, it's Dream's sense of responsibility that will be his downfall. Night doesn't care. She knows, because she promises they will never meet again.
Why is Night so callous? She is as old as Time, and yet she eats continuously. Inside her there is a void that can't be filled, a black hole that pulls at everything, a pall that consumes every ray of light, an addiction, an endless hunger. Next to that, love for her family runs a distant second.
The gods have their problems, but they usually end up as constellations or strange animals. Gaiman leaves Night in a hell of her own making, willing to lie to her own son and let him go to his doom.