So I want to start by saying that I do think this is a clever game idea, so don't take any of the following criticism too hard:
For me the biggest issue was that each failed level kicked you all the way back to the first. I was getting a bit into the game once I finally got a feel for it, but then I'd mess up and have to replay the same easier levels again and it was kind of frustrating.
The next thing I ran into was the fact that you can't anticipate the other car's movements and so often the levels become more about memorizing which cars move where to perfectly execute each level, which at face-value could really work in your favor (extremely complex levels where the whole point is re-trying until you've figured out and memorized the correct pattern), if not for the problem above. As-is the ability to determine which direction the other cars will turn would be a really worthwhile addition and make each level more approachable from the outset.
Finally, I feel like the concept doesn't quite hit the theme. I understand the justification from the description above, but I feel like in-execution this is a solid foundation for a project, but maybe not one themed on "Joined Together."
Regardless, you should be proud of everything you managed to do in 2 days, and I think with some simple tweaks this could be a great mobile game should you choose to continue working on it.