The side cut of a short radius ski is designed to make the ski turn. If you put them on their right edges, they turn right. If you put them on their left edges they turn left. Ski hills are not perfectly flat; they have irregularities in the snow. If you try and keep your skis perfectly flat and there is a slightly higher surface on the left side than on the right side of the ski as you go by, this is just like putting the on its left edge. If there is a slight mound on the right, this is like putting the ski on its right edge. You may not notice the slight local curvature of the surface, but it's there, and it's random, and your skis will notice, and try to interact with it.
I suspect the problem isn't so much of a problem on your girlfriends skis, despite their equally short radius because her skis aren't as high-performance as your skis, but I am not familiar with them, so it's only a guess. Put on some gloves. If you grab her ski with one hand at the binding and one at the tip, how much can you twist it. Did you cut your hand on her sharp edges, 'cause you forgot the gloves? Are the edges sharp all the way to the tip?
A high performance ski is stiffer in torsion (harder to twist) and will react more strongly to being put on edge, and also will react more strongly to irregularities when running "flat".
A ski with a high performance tune (sharper, more acute angle, less base bevel, no detuning) will react more quickly and more strongly to being put on edge and require less of an angle before it interacts with the snow; it will also react more strongly and require less of an irregularity in the snow to react.
There is nothing wrong with your skis, and your skiing may or may not be excellent. You will probably get the most speed and carry the most momentum to get up that next hill if you keep them carving on a slight edge. If you are going too fast to carve a turn a clean railroad track turn at their side cut radius, then keeping them on edge will keep them stable, but you will have less drag if you run them flat and let them wobble.
This "hunting for turns" instability is caused by the short radius side cut, and not to be confused with the vibrational instability (where you skis feel like a paint shaker on crack) that in days gone by could only be banished by big long heavy stiff skis.