If a character is speaking aloud, the dialogue should be within double quotes (assuming this is American-style English usage and not British-style usage, as you used American style in your snippets in comment #4). If a character is reading aloud from a book, he is essentially quoting someone else. Therefore, using single quotes within double quotes would demarcate the quoted (read aloud) text. Example:
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Grandma opened the book and started reading. "'Petunia was raised on a ranch in a sad little town called Gloomy Gulch. Many years had passed since the gold mine had turned barren, but her family was determined to find other ways to keep their land.'" Grandma looked up at me. "I can already tell I'm going to chuck this book against the wall by the third chapter."
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I would be concerned about how long the passages are that your character is reading aloud, and how critical all that information is to the story. You might consider having the character only read aloud the salient portions that need commenting upon by either himself or another character, and prose your way through the rest. Sometimes the act of telling isn't a demon, but a pace-saver. Example:
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Grandma opened the book and started reading. "'Petunia was raised on a ranch in a sad little town called Gloomy Gulch. Many years had passed since the gold mine had turned barren, but her family was determined to find other ways to keep their land.'" Grandma looked up at me. "I can already tell I'm going to chuck this book against the wall by the third chapter. Shall I continue?"
"Sure, why not," I said. "Netflix is down."
It wasn't too horrible until Grandma came to the part where the author described Petunia as having raven hair, cerulean eyes, and flawless skin, with a mention that the character was so achingly beautiful that it was a curse rather than a blessing. My chicken soup threatened to make a return trip from my stomach. "Can you skip to the part where the evil sheriff shows up to shove Mary Sue down an abandoned mine shaft?"
Grandma laughed. "It doesn't turn out that way. Here, I'll skip to the end. 'And then Petunia and the evil sheriff's long-lost identical twin brother rode off into the sunset and lived happily ever after. The End.'"
I wrinkled my nose. "I like my ending better.
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I hope that helps.