Hard shifting is most often corrosion on the cables. Kids bikes get the galvanized cables and they corrode quickly.
The quick fix is to shift the bike up onto the big cog in the back, then with out pedaling shift to the smallest cog. This will give you enough slack to pull the housing out of the stops. Now you can slide the housing over to expose the cable. Sand it down and lube with a light oil. Stick everything back to gether and you should be OK.
The gripshift is easy to take apart if you know how. If you don't know how there is a 50/50 chance of breaking the retaining tab. Try to get someone in a shop to show you how to do it.
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