As part of the project I was thinking we will skip game engine altogether because I wanted to teach my son a bit more about how to structure the application, etc. I thought in future we would use a ready game engine but at least once we would go through the exercise of implementing everything.
Everything was fine until we approached the problem of collision detection and handling. That's when things went downhill pretty quickly. Even with my theoretical math background I was soon consumed with just enormous amount of corner cases and finally decided to relent and use Box2d for this.
I am not a professional game developer, but I have over 20 years of development experience + math background and I still made the mistake of underestimating the problem. It really seems easy problem when you state it and just becomes exponentially more and more complex as you start digging into details.