Thank you so much for the feedback! That is indeed a known bug we plan to do another polish pass once judging is over and that is at the top of the list. We know that the mouse capture bug can make it even more challenging, but we were inspired by the original Lunar Lander game as well as KSP in how the lander controls. It is meant to roughly model actual mechanics of having small control thrusters like an RCS module that help with rotational control but do not auto-cancel the rotation of the craft, and a large powerful main thruster for delta-V maneuvers.
A “stability assist module” was a planned upgrade we did not have time to implement, and will likely add post-judging period.