No. They're cousins. Emmeline addresses Arthur Lestrange as Uncle, while Richard calls him Father.
Plot Synopsis from IMDb:
In the Victorian period, two children are shipwrecked on a tropical island in the South Pacific. With no adults to guide them, the two make a simple life together, unaware that sexual maturity will eventually intervene.
Brooke Shields was just 14 years old when she filmed The Blue Lagoon, the infamously sexy and slightly salacious island-set romance that capitalized on burgeoning hormones in a big way.
The film was shocking when it debuted in the summer of 1980—but even more than three decades later, it can still make jaws drop.
Here’s a look at some of its more compelling tidbits, complete with undiscovered iguanas and a nifty trick to cover up nudity (from Mental Floss).