How we cite our quotes: (Chapter.Paragraph)
Quote #1
The hot, tangled ball of anger inside of her turned inside out. Azalea fell to her knees and began to sob. Hacking sobs, so hard it hurt to breathe. She buried her face in her hands and couldn't stop. Every time she tried to say Mother, the word broke in her throat. Mother, incomparable Mother! (3.9)
Azalea's grief at her mother's death is pretty overwhelming—she can't speak, she can't stop crying, and she can barely process that it's actually happened and it's real and she'll never see her mom again. Also, note that she's alone when she collapses like this, so in one sense this helps her get it out of her system so that she can comfort her younger sisters when she sees them next.
Quote #2
"Aye, sir, but th' princesses, they've been eager to see you, sir—"
"I cannot abide them," the King snapped, in a loud-enough whisper that it echoed in the hall. "I cannot! Keep them away from me, Mr. Pudding!" (3.62-63)
Why can't the King stand the thought of his daughters right now? Probably because they'll remind him of their mother, his wife, who he's just lost. And obviously, he's not dealing with that loss too well right now. Then again, how one grieves is a very personal thing—it just might be nice if the King didn't emotionally shut out his own family in the process.
Quote #3
Eathesbury tradition required the steward of the family to sit up the first night to watch over the deceased, but Azalea could hear Mr. Pudding's hacking sobs from across the palace, and she joined him in Mother's room, pouring cups of tea to soothe him. (3.80)
Here's another tradition, outside of mourning, to help people navigate their sadness when someone dies. This seems like a way of paying your last respects to the deceased, or saying goodbye to them before they're buried—it won't make the sadness go away, but maybe it helps just a little.