Enid Blyton: Faraway Tree/Wishing Chair, some of her short stories. She might even find The Secret Island good or some of the school ones.
Some Noel Streatfield's like Ballet Shoes. Like Enid Blyton she wrote some lovely gentle family stories, but also some adventure ones.
Would she like ballet stories? They're not really entirely about ballet, but around it.
"Lucy Jane and the Ballet" is lovely, and I think there's more in the same series./
There's a set of ballet stories by Antonia Barber called "Dancing Shoes", the first one is "Lessons for Lucy". It's more about friendships than ballet, really.
Little House in the Big Woods is another gentle one, but you may want to read it with her.
The Bullerby Children
Milly Molly Mandy
Naughty Little Sister
Family From One End Street
All ones that don't really get scary, but may need a little explanation as they're historic now.
There's also the dreadful Rainbow Fairies if those aren't too twee for her. My ds, persuaded to read them by his sister and much preferring adventure, gave it the lovely backhanded review: "When Jack Frost (the baddy) appears it was almost interesting." which I think says it all.
I do feel your pain. My middle dc loved reading but wouldn't touch anything she thought was scary for years. What I did find was 1950s/60s school/real life stories were her love. She's just gone off to university and one of the books she took was "Coronet for Cathy" which is her absolute favourite. I had to track down a second copy for her.
The stories in that era were much gentler in a lot of ways. Nowadays publishers want there to be a big event, something for the main character to work towards. So looking at older books may give you more what you're looking for.
I'd avoid the Daisy stories by Dick King Smith. They're often recommended on here, and I see exactly what he wanted to do with the character, but actually she's a rather nasty little bully who gets what she wants. They upset dd quite a lot.