A dangling modifier is a phrase or part of the sentence that intends to modify a word but is not linked to it in a correct and logical manner. In this case the dangling modifier is "Sprouting pumps of water through their trunks". It is placed next to the children which could mean that it modifies "the children" but that makes no logical sense since children don't have trunks. We have to assume that the word it is intended to modify is elephants but the modifier is missplaced.
In order to correct this you have to rewrite the sentence. These are some of the options that I came up with.
1) The elephants are sprouting pumps of water through their trunks, which makes the children giggle.
2) Sprouting pumps of water through their trunks, the elephants make the children giggle.
3) The children giggle at the elephants because they are sprouting pumps of water through their trunks.