negation - How to reply the two different questions, "Don't you want to play with me?" and "You don't want to play with me?"

I know similar questions about how to answer negative questions were asked before. But still I am confused.

If somebody asked you "You do not want to play with me?", I thought it's correct to answer "Yes, we do want to play with you", or "No, we do not want to play with you." But then I read this sentence in my daughter's picture book "Elephant and Piggy" (the author is American), they answered "No. We do want to play with you." So I asked one of my American friends, who told me it's correct. My friend said if the question was asked as "Don't you want to play with me?", you have to answer in another way, like "Yes, we do want to play with you" and "No, we do not want to play with you".

From Can I Play Too? by Mo Willems