I also have a small hand, and can barely reach a 9th on the piano. Fourth finger was hard for me at first, as it is for everyone else, but eventually I obtained strength in my pinky and am now at the point where my 4th finger vibrato is noticeably better than 1st finger!
Perhaps it is the distance between the third and fourth finger that is really the hardest thing for you. Would playing in the key of A on the G and D strings help?
Otherwise, switching instrument sizes is probably in your best interest. In case you’re not aware, 7/8 is a size often used by petite adults.