A reliable, quality autoloader fit for small hands and under $450 is a steep order.
Have you tried or looked at a Ruger P95? It's a larger gun, but should fill the bill in (most) all of the other areas.
You might find a used XD or Glock 19 for around/under $450 if you keep your eyes open. Stick with the 9mm for less recoil, less expensive shooting, and a lower cost on most used guns.