My guess would be that there's a burr inside the blade stanchion section that's cutting her hand. I put clear packing tape on the blades of all my skaters and children. Two layers cover the unfinished edge inside the stanchions and protect from burrs and cuts. Clip the curve to make it fit that part of the blade.
Just be sure you trim the tape so it doesn't get near the business edge of the blade. I remove the tape entirely before the blades are sharpened, just to be sure it doesn't get in the way of the sharpener. (More to ensure that I don't get any comments about it being an obstacle. :dramaqueen: )
On spirals, the foot doesn't really move very much, but on catch-foot spins and twizzles, there is more movement and force, so that could be a secondary cause of the cuts. If she pressed with one side of the blade more than the other, the friction can open up a cut.
Are you sure your DD is catching the same foot in the same place each time? Many skaters use different grips and even change feet from element to element. For example, I have a skater who does her catchfoot and y-spiral with the right foot on the ice, but her catchfoot spin is done with the left foot on the ice. Most people would assume it's always the same blade being "caught," but it isn't, which is why I taped both her blades.