Hello Pawel,
I just looked at your files, some remarks:
Only use one mesh for the robot cell (or use Mesh Join to combine them!), at the moment you generated two robots which really slowed down KUKA|prc.
The problem with A4 is because you are moving through a singularity where A4 and A6 basically share a rotational axis. It's best to solve that by tweaking the position of your object in relation to the robot. In your case, setting the base to 100 in X and 140 in Z (40 was set by you) solves the problem. I've then also set the Initial Posture (next to the start/end position) to "010" and it now looks fine.
Alternatively you could also experiment with the angle of your tool to solve singularities.
Ultimately, I usually recommend against using SPLine movements, as they are splines that are not defined geometrically (e.g. Bezier curves, Akima spline etc.) but calculated by the machine in realtime to achieve a smooth motion through a set of points. A spline may look different depending on which robot you are using. Consider using simple LIN movements instead, they are the most simple and robust movements. Otherwise just be prepared for possible differences between the simulation and actual robot movement.
Hope that helps!
Best,
Johannes