Originally Posted by Боб Уайтман
Yes, those two sentences are correct. But they may have different meanings:
Я часто читаю русские рассказы для детей. - The main point here is "рассказы для детей" - stories for children. That does not necessarily mean you read them TO children: you may read "stories for children" alone, just to learn a language. Or, maybe you like "children stories".
Я часто читаю русские рассказы детям. - The main point here is "читаю детям". It means you read them aloud, and children listen.