If it's for kids and you're not looking to get it back, hit it with sandpaper and paint it their favorite color. They'll love it and you really don't have to do much more then shake off the flakes.
Woodworking
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This is what I'd do as well, paint will be a lot less effort and a whole lot easier to touch up as it gets used. Plus the kid can paint their own patterns or emblems or logos or whatever on it
Forget the chemicals, you'd need to be an expert to insure a good finish after strippers. Sanding should do nicely and not be too hard - it's also one of the steps kids can help with. From the looks of it sanding by hand or with a jitterbug should be enough. Sand with the grain. Maybe 120-150 grit until it's uniform and then 220. Use a tack rag to get the dust off. Then stain if you want and then the poly, at least 3 coats with a very light sanding between them - follow the instructions on the can.
As it's for a kid, I'd suggest using some water-based and toy-safe acrylic paint.
It’s for your kid. Put in the time and make it look nice. Maybe get them to help too.
I think their point is that it's for a kid, so it's not going to stay nice, so no point having it start out perfect