This should answer how the White Diamond's Pearl got cracked.

As much as they didn't want to, the Yellow Diamond knocked on the door of the White Diamond's quarters, the Blue Diamond right beside her.
Despite reluctance on her part, the White Diamond answered.

"Something's wrong with the Cluster, we're gonna go check on it," said the Yellow Diamond, "You wanna come?"
"Hmmm..." thought the White Diamond, "Nah. As much as I'd like to see the Earth out of the picture, like you, three diamonds at once might accidentally throw the Earth out of orbit."
"She's got a point there," said the Blue Diamond.
"Right. Let's go," said Yellow.

They turned to leave, but the White Diamond made a noise, advising them to turn back in her direction.
"I've been thinking about the Rose Quartz thing as much as you," she said, "Your Zircons are right; something doesn't add up."
"Really?" queried the Yellow Diamond, "Then what do you think happened?"
"Well, there's always a possibility that...Rose Quartz and Pink Diamond are...one and the same."
The other Diamonds were befuzzled. But then their faces changed to one of disbelief.
"Think about it. Us Diamonds don't shatter that easily. For all we know, those Pink Diamond shards aren't our Pink Diamond's!"
"You're putting us on," exclaimed the Yellow Diamond.
"What makes you think we'd believe everything you say?" said the Blue Diamond.
"Hey, I'm a Diamond, just like you!" said the White Diamond, "Besides, there's 20 big ones in it if you prove me wrong!"
The Yellow Diamond thought about it for a minute.
"Okay, you're on. 20 big ones. C'mon, Blue."

They turn to leave once again. But this time, it's the Yellow Diamond who decides to turn around back to White.
"You do know what this means, right?" She said.
The White Diamond shook her head,
"We're leaving you in charge of Homeworld while we're gone. That means this place should be the same as it is now by the time we get back. Also, keep an eye on your Pearl, cause we don't have any healers since we poofed and bubbled all our Rose Quartzes. The last thing we want to see is our fellow diamond's pearl's gem cracked."
"...Sure," said the White Diamond.
Now the Blue Diamond had something to ask.
"Do you need us to get you anything while we're out?"
"Get me a pizza." All aliens love their pizza.
"All right. Bye."

This time, the Yellow and Blue Diamonds were gone for good.
"They're gone, My Diamond," White Pearl confirmed.
"Very good," said the remaining Diamond, "Pearl, you know of that turntable we confiscated from one of the Zoo humans?"
The pearl nodded.
"I think it's time to test it out."

The pearl ran off to retrieve the desired device. The White Diamond pulled out a staff from her gem. Her pearl came back, and turned it on. A "record" was already inside, and it began to play. The White Diamond started to sing into her staff as if it was a microphone.
Just take those old records off the shelf
I'll sit and listen to 'em by myself
Today's music ain't got the same soul
I like that old time rock 'n' roll!