Many would-be pianists have told me that they stalled out on the piano because they just couldn't get their two hands going at the same time. "First I learn one hand," the story goes, "and then I learn the other, but I can't stick them together!"
The thing is, that's not how pianists think. Flute, saxophone, trumpet - these are instruments that can only create monophonic (i.e., one note at a time) textures. The very nature of piano is polyphonic (many voices), and most of the music written for the instrument takes advantage of this.
But polyphonic does not equal "monophonic plus monophonic" - you can't just learn the parts separately and mash them together. You'll need a different strategy.