You could use different scoring for the kids and the adults. The normal scoring is
Word length 3 4 5 6 7 8+
Points 1 1 2 3 5 11
For the less skilled players, you could try something more like
Word length 3 4 5 6 7 8+
Points 2 3 4 6 10 15
which increases the reward for finding any words not found by the veteran players, and gives huge bonuses for large words (which are even more unlikely for them). You can adjust the values up or down depending on the relative skill levels of the junior players.
Another idea, related to Don Kirkby's interesting answer, is to automatically score words over a certain size for the juniors (instead of discounting them if others have them) - for example, any word over 5 letters. This encourages the children to put the effort in for the larger words, which for them is likely a much more challenging task than for the grown-ups.