my hands are probably large rather than small, but amid my instruments I have one which I really like with 550 mm scale - and I play it often and love it.
I use general normal tension d'addario for it.
I suspect that in your case it is a guitar problem, not strings.
Something wrong with guitar.
Buy another small, but nice instrument for her if this one do not work
I ordered some D'Addario hard tension carbons. According to info at the SBM website, these are the smallest in diameter on the treble strings. We aren't dealing with a guitar problem really it has had a new saddle and nut made for it, but I will possibly have to do this again if the string slots are too big. I will probably lower the saddle a hair, but the problem that my wife has is that her fingers aren't very big around. And not having very much flesh to work with on them is the problem for her.
The treble strings that we have tried are too big around and leaves huge grooves in her finger tips. She tells me that her finger tips hurt after playing.
The last set we tried was Augustine Classic Blue, which were huge. And yes, I would prefer it if we could get her a better guitar, but left handed, fractional sized guitars are hard to come by, short of commissioning one, and that would cost a small fortune. Her guitar is Chinese made, and is a right hander that was converted to lefty by a luthier with a new nut and new bridge with properly compensated saddle. 50mm nut. I wish she could play a full size guitar, but the body would be too big. Of the lower tension strings I tried, EJ45 D'ADDARIO were the most comfortable trebles for her, as there really wasn't much tension being on a 610mm guitar. But the strings were too sloppy and loose feeling.
My wife used to have a Taylor GS Mini (steel string) and actually she felt this was more comfortable on her finger tips as the strings were so small in diameter, and there was less tension being short scale. We both hated the sound of it though (classical just sound better).