Middle Grade Book Homeschooled Girl

Looking for a middle grade novel I read 10+ years ago. Details are:

- published around or before 2012
- middle grade fiction
- main character is a girl with divorced parents
- she keeps getting in trouble while living with her mom and is sent to live with her dad and his new wife and her younger half-sister
- dad might live in Ireland, or Wales? I remember the main character has to learn a different language at her new school, and I think it was Celtic origin or something similar.
- she has a bad time at her new school, and instead does her own homeschooling with a project about the area they live in - flora/fauna/history etc
- she meets a strange boy who rides a horse (and they might have a romance)
- she runs away at one point
- there is a scene where she eats strawberries and her dad finds out she has a pierced tongue
- her younger sister asks her to pierce her (the younger sister's) tongue and it goes wrong and they gets in trouble

I don't remember anything about the author or title or cover of the book. I've been looking for this book for years and years. Thanks!

Scarlett.