What is Reddit's opinion of Coming Out Atheist: How to Do It, How to Help Each Other, and Why?

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I strongly reccomend your cousin gets hold of a copy of Coming Out Atheist: How to Do It, How to Help Each Other, and Why by Greta Christina.

Possibly even get a copy yourself.

This excercise with your aunt? That may be fun, but I wouldn't expect it to be useful. And it may even be harmful.

You and your cousin may look at this as a fun way to get a cool gotcha moment to convince your Aunt to change her mind. But to be perfectly honest, that should not be the goal.

The goal should be for your cousin to be safe and not living in an oppressive environment.

If she's already safe and the Aunt isn't that big a deal then things are probably alright. But the way you've described the situation is setting off alarm bells. It's possible I'm overreacting given how little I understand the situation, but it worries me.

That book has a lot of good information around how to deal with family members and, if neccesary, how to get out from a bad family situation and set yourself up independently from them.

Strongly reccomend the book over the apologism excercise.

That said, my favorite gotcha question to Catholics is: In the bible, Matthew 5-13, Jesus says that we should only pray in our closets using the Lord's prayer. Have you ever prayed publicly, and if so, why did you go against Jesus' explicit instruction in that matter?

I think this book may have some insights and suggestions for you. It's a very balanced look at how to come out as an atheist.