I can't remember the brand name, but the aerosol paint stripper they sell at Wally World has worked well for me in the past. It strips quick and through multiple layers. I spray it on, let it set for 15-30 minutes, and hit it with a scrubby pad and the waterhose.
Unless the little one has her heart set on a specific shade, I would also suggest one of the textured spraypaints on the market. I have done several stocks with them, and they feel great. Let it dry several days, coat it with the desired finish of clearcoat (satin, gloss, matte, etc...), let that dry several days as well. Surprisingly durable.
Les