Well, 'peep' can mean to look quickly or secretly. So'mom let me peep stories' might mean that mom is allowing you to quickly look at or secretly read some stories. Maybe it's like she's giving you a little peek into a book of stories.
The 'Bo Peep' story is often about a shepherdess. In the nursery rhyme, 'Little Bo - Peep has lost her sheep'. It's a simple children's tale where Bo Peep loses her flock of sheep and then goes to look for them. Eventually, she finds them again. It's a charming little story that has been passed down for generations, teaching kids in a fun way about the idea of losing and finding things.
There was a mom who liked to peep into her daughter's room. Not in a nosy way, but because she was always amazed by her daughter's creativity. One day, she peeped in and saw her daughter making a beautiful collage with pictures from their family vacations. It made her heart full of joy.