From her father's perspective (who didn't know Satsuki saw the corpse, premonitory or not), it would be extremely plausible to imagine Satsuki's mother was fine when the girl got home and she was too absorbed in the games to notice when she collapsed. "Why didn't you do anything?" is kinda... The fuck did you expect her to do?? She's in middle school, she would have freaked out. As the parent, I would think that maybe it was for the best that she did not notice when something happened at the time it did, because no one is truly prepared to witness the death of a loved one like that, let alone children. It requires cold blood to act wise in that situation, I doubt a 13 year-old would have that.
But, in all honesty, I believe this is what Satsuki's father thinks >now<, if she didn't try telling him about her mother's corpse. Any premonitory corpse that showed up later could be just seen as an hallucination due to trauma (I am not a psychiatrist tho).
Maybe, just maybe, she tried lying saying she haven't noticed anything but lying about it all filled her with so much guilt that she decided it wasn't worth it. Specially with her father resenting her for awhile (which ok he has the right to do so unconsciously but is kinda fucked up to do to your child).
Also, I am really curious to know the cause of death. There is bleeding in her chest, but what could have possibly struck her in a way that became fatal? A mere shard seems unlikely