One might suggest that rather than what they "could do," the adults should have focused on what they could avoid doing that would have saved Paul from his early death.
Because of the fact that they "feel superior to everyone in the neighborhood," and so must always be living in a very fine style, the adults in the house are concerned entirely with money. The father is worried about it but cannot come up with any more of it, the mother is worried about it too but also cannot find a way to make more of it. But they still must maintain their fine lifestyle and so the phrase "there must be more money" constantly rings throughout the house, even when it isn't actively spoken.
Without that constant pressure to find more money somehow, it is unlikely that Paul would have been so concerned as to drive himself into a frenzy to find out the winners of the horse races each time. Young children are not likely to be as obsessed about money as adults unless it is shown to be the most important thing, the only way to please their parents which is what Paul hoped to do by being the one to have found more money.