In Chapter 1:
"
At nightfall, the little girl borrowed her father’s telescope and peered into the sky. She looked and looked, but she saw nothing. Hours turned into days and then years, but still the sky revealed nothing. Finally, the little girl sighed and said to Luma, “If we stay here looking much longer, I’ll be an old lady soon.” But then she had an idea. “Why don’t we go out there and find your mother ourselves?”"
This part lets us know that a long time had passed between when Rosalina first started looking for the Luma's mother using a telescope, and then finally deciding to travel through space to look for her. However, how could Rosalina, a child, just up and leave like that if her parents were present? How come we never see her ask for permission or assistance from her family?
In Chapter 4:
"When she awoke, the girl’s face was damp with tears. “You have Star Bits in your eyes!” said Luma to the girl. Wiping her face, the girl replied, “These are tears, not Star Bits. I’m crying because I’ll never see my mother ever again!” At this, Luma began to cry too. “Mama, oh, Mama… waaaah!”
The pair traveled through the starry skies, and though they encountered many other comets, not one of them held Luma’s mother. Luma was despondent. “Now, now, Luma. The rain clouds won’t go away if you keep crying,” the girl said, giving Luma a squeeze. “I’ll give you a present if you stop.” The girl closed her eyes and said gently, “I’ll take care of you.” With these words, she felt a small spark in her heart."
This part is the first definite hint that her family are dead - Rosalina claims she can't see her mother ever again. However, at this point, the story keeps things ambiguous. It swiftly dismisses her crying episode and makes it come across as somewhat of a playful scene. It's meant to fool us into thinking Rosalina is just homesick, and is quickly cheered up by Luma. This is likely meant reflective of her own attitude - she fooled herself into thinking her parents were alive.
And finally, all of Chapter 7, is very important:
After seeing their 100th comet, a sudden thought popped into the girl's head: “I wonder if my homeplanet is still as blue as it was.” That’s when she remembered her father’s telescope.
Peeking into the telescope, a tiny blue dot floated into sight. It was smaller than a Star Bit. “How strange… It’s so far away, but it feels so close.”
She twisted the knob of the telescope, and the blue dot grew until she could make out a grassy hill dotted with flowers. It seemed very familiar to her. Zooming even closer, a terrace on the hill came into view. “I used to go stargazing there when I lived on my home planet.”
She remembered rubbing the sleep out of her eyes as she followed her father up that hill to look at the stars…
She remembered how she and her brother would sled down that hill…
She remembered having picnics with her mother on that hill on bright and windy days… And…
"I want to go home! I want to go home right now!" The girl burst into tears, and the Lumas didn’t know what to do. “I want to go home! I want to go back to my house by the hill! I want to see my mother!” The girl was shouting now, her face wet with tears. “But I know she’s not there! I knew all along that she wasn’t out there in the sky! Because…because…”
"She’s sleeping under the tree on the hill!" The girl’s cries echoed through the stars, and a hush fell over the area.
This entire chapter is the point where we find out her family has passed away, for sure.
But notice, when Rosalina starts recalling how she spent her time with each individual family member, each thought relates specifically to "the hill".
Then, when she comes to her mother, her thoughts begin to bring up another memory, signaled by the "And...".
However, she breaks down as soon as this memory comes up in her head. Then, at the end of her crying state, she reveals:
"
I want to see my mother!
But I know she’s not there! I knew all along that she wasn’t out there in the sky! Because…because…”
"She’s sleeping under the tree on the hill!"
The most important part is "
I knew all along that she wasn’t out there in the sky!", because that tells us she WAS searching for her own mother as well as Luma's, and probably the rest of her family too.
What's also important is how she knew where her mother's resting place is - if the mother had died AFTER she left, she could not have known this. What's more, it took her repeated memories pertaining to the hill to get to the memory of how her mother's corpse is buried under the hill. Which shows how she truly had locked the memory of her family's demise away.
Some might say this only means the mother was dead before she left, but again - she NEVER contacted her father or brother before leaving. She never introduced them to Luma - she believed they were just gone away, as she was far too young to understand what death is. Heck, even in Chapter 7, she still can't fully comprehend it - she refers to death as "sleeping". But she definitely realises this isn't just regular sleep.
I'm actually surprised I have never seen anyone mention this anywhere. It's pretty clear, but I guess since all of the details are spread out, people don't notice - I also think the "this is a Mario game" mentality is also why nobody notices this point. This adds a whole new level of maturity and darkness to Rosalina's Story, and it's also a very realistic representation of the mentality a child might have when dealing with death before understanding it. Most people accepted it to be a sad story, but this just makes it crazy deep and really, one of the most depressing things I've ever seen in a video game. And a big part of why I love the character.
I actually would like to know what happened to her family in the first place, but I can understand why Koizumi didn't detail this - it would make the theme of death very direct. Keeping it subtle means young children won't draw too much from the story, but adults will realise the severity of the situation. It's actually masterful writing technique on his part. It's very much a hidden element to the story.