Why not sell child tickets on the TVM? For that matter, there should be shortcuts for common combinations like adult+child, 2 adults+2children to the same destination (preferably offering a discount, but that's another issue).
The London Underground TVMs definitely offer children's tickets. As far as I remember, their automatic barriers make a different sort of beep when a child ticket is entered, so an adult using a child ticket should be spotted fairly quickly.
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