After fiddling around with planet editor I realized either Yavin Prime is like maybe 10 times larger than Jupiter or either Yavin 4 is almost up on the face of Yavin Prime (closer than Earth-Moon distance. about 250,000 km or so). :P
Doesn't seem that impossible; Mimas, Enceladus, Miranda, Ariel, and Proteus are all closer to their planet than that and fairly major moons. Since Yavin's moon is clearly made of rock, it's likely to have a high density and therefore a Roche limit closer to Yavin's surface too.
Also, the FOV in the movie might be smaller than SE's 45 degrees. At 22 degrees (a more or less realistic FOV if you consider your screen a window out of a spaceship) Jupiter looks about the right size in Io's skies.