Will disneyland be crowded in late July on Saturday?

Your dad is right (so far). This summer has had very light crowds compared to past Summers. The gas prices probably have a lot to do with it, keeping a lot of the semi-local people(Central/Northern CA, AZ...) away. I don't know if it will last, but unless there is a sudden influx you should be just fine. The park won't be empty, but you also won't have huge wait times either.