What's the Name of That Book??? discussion

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SOLVED: Children's/YA
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SOLVED. YA fiction. Girl named BabyGirl (?) and her mom run away from abusive husband at the height of the Elvis craze. [s]
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I read this book in the mid 2000s (2003-6?), and it was probably an early teen or YA fiction book. The book takes place in the 50s when Elvis was really popular. Main girl was named BabyGirl (pretty sure but could be a variance on that) and hated her name. She and her mom run away from the abusive father (who has tried to suffocate BabyGirl) in the middle of the night. BabyGirl is probably 13-16. She has a big old crush on Elvis and thinks about him a lot. She starts school at a new school and is friends with twin girls, one of whom is well-endowed and the other who is very flat-chested (this is how people tell them apart). One of the twins has a crush on a boy called Rooster, and later they have sex and she gets pregnant. In the end I believe BabyGirl's abusive father finds them.