This is Nightmare Fuel for Mario players in itself, but a commentor provides a sad reason why Peach does not remember mothering Bowser's children:
skim172: You'd think Peach would remember having sex with Bowser. Or at least, giving birth to a giant spiked turtle. Eight times.
Unless she's suffering from intense psychosis brought on by the trauma of multiple kidnapping, torture, and repeated rapes. She blocked out that part of her memory as she's blocked out so many things. It's a defense mechanism. It explains why she's always kind of spaced out; she's not an airhead - she's disconnected from reality, because that's the only way she can cope.
Think of Super Mario as the world ... viewed through the eyes of Peach - not a princess, as in her delusions, but a sexually abused and tortured woman with a shattered psyche. The real world hurts - instead, she imagines a cartoon world with talking mushroom people, smiling plants, and fire-flowers, where she's a beloved royal figure - and she can fly. Free as a bird.
And out there is a hero - a paunchy middle-aged plumber, perhaps representing a father figure - fighting through legions of enemies to come rescue her.
But she never does get rescued, does she. On those brief resurfacings to reality - she's still a prisoner of that evil man. Bowser. And so she returns back to the dream - another adventure for the heroic Mario, to come save daddy's little princess.