As you notice by default right mouse button fire left panel weapon, and vice versa, which is very unintuitive.
That's how to fix it:
1)
Go to settings -> ship control -> weapons, and swap mouse buttons
set primary fire to mouse 2, secondary fire to mouse 1
2)
Set weapon what you want on right side as a PRIMARY, and what you want on left side as a SECONDARY
3)
On this example right mouse button fire lasers, left mouse button fire shards.
I hope that I could help, o7