Despite this movie being a sequel to Journey to the Center of the Earth (2008), Josh Hutcherson is the only actor to return from that movie.
(at around 46 mins) The scene when they are walking to find the submarine, you can see the wide open space where they filmed Jurassic Park (1993). That open space is where the dinosaurs are on a stampede.
The original Jules Verne story, Journey to the Center of the Earth (1864), on which Journey to the Center of the Earth (2008) was loosely based, never had a sequel. However, another Jules Verne story, 20,000 Leagues Under the Sea (1870), did have a sequel, called "The Mysterious Island", which was released in 1874. The book followed five American men stranded on an island in the South Pacific, which is similar to a plot point in this movie.
There is another Jules Verne novel titled "The Golden Volcano", which, although is set in the Canadian Arctic during the gold rush, spews gold nuggets when it erupts. This is likely where the mountains of gold came from for this movie.
It was Dwayne Johnson's idea to sing and play ukulele in the movie, as he'd grown up in a musical family where this was part of their Polynesian culture. He pitched it to the director, Brad Peyton, who loved it as a means of revealing the fragility of the characters and getting them to bond.