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Also think about the hand shape, getting the child to make the "shape" of the chord with the hand in the air. Then change to the shape of a different chord.
Other things to think about are:
Would turning the wrist slightly to right or left help?
For certain chords, would playing further IN on the keys (so the fingers are playing inbetween the black keys) help?
Is the child sitting at a sensible height (not too low)?
Are you sure the child knows exactly which notes he/she is supposed to be playing? Get her to name them.
There are some exercise for finger independence in the Dozen a Day books, which might also help. One exercise which I like is to simply hold down one note with a finger and keep it held down, whilst playing the adjacent note/finger repeatedly (so hold down middle C with thumb and play D with finger 2 say 10 times, then try holding down ,say, D and playing E etc). This might help with lifting fingers out of the way when they are not involved in the playing of a chord.
There are also lots of other exercises for chord playing in the Dozen a Day range. These books, which have been around for years and don't seem to have dated at all, are brilliant for helping with all sorts of problems. My pupils love using them!
Good luck and if all else fails, try finding some pieces that DON'T contain chords, for a few months!
Alright, the main negative bit is it's not a piano.
BUT, if it spurs the child on to play the piano once he/she begins to appreciate its potential, this may well be one possible approach..
I have always found when teaching small children that it is easier to get them to put down one note of the chord, hold it down and then add the other. They then get the "feel" of how the chord should be on the keyboard and can then usually replicate the complete chord within a few tries.
Beware twisting of the hand or over curving of the fingers - this can lead to bad habits and eventual damage includeing RSI and carpel tunnel syndrome.