Hey, I have an 03 Tiburon and mine does the same thing when I fill it with gas. I found the last time I pumped my petro that if I adjust the insertion and angle of the nozzel, I get much better results. But still I can not hold it down full pressure, otherwise it does that annoying stopping thing. So either way, I end up taking way longer than I need to to fill up.
Sorry, I have nothing to offer you about your check engine light aside from taking it to an authorized Hyundai dealer/mechanic to have it looked at.
Good luck.