It was an interesting premise but the "surprise twist" was telegraphed well in advance at least for anyone who bothers to think about it at all.
If you're trying to repopulate the world then you don't just save your family, that's far too limited a gene pool. Even a basic knowledge of science would tell you that.
And kids as food never made any sense. Quite apart from the moral/ethical objections, it doesn't make any practical sense. For one thing they'd require food to stay alive. A lot of food. More than they could possibly provide.
There are just so many basic logic problems that the story doesn't hold up to even a cursory examination.
It's too bad because I think the premise was promising. I'd thought it might be a taken on a Fallout vault type of situation. I was hoping for a well thought out look at what it might be like to live trapped in close quarters with a small number of people for years and how that would affect people psychologically but unfortunately that was not this book.