Peach's Nair is guaranteed to ALWAYS cancel Din's. Peach's dair, fair, uair, bair, parasol, and toad can also cancel 100% when done properly (it requires better timing and spacing). Ideally, Zelda won't be using Din's Fire near Peach so even if Zelda detonated Din's early, the ending lag and distance from the opponent would prevent follow ups.
There are very few moves that can't always cancel. One notable attack would be Sheik's Nair. Sheik isn't able to cancel a fresh, fully charged fireball but if Din's isn't fully charged or not completely fresh, then Sheik can cancel it.
Every character, minus Ice Climbers and Olimar have a skill that can cancel Din's Fire. Of course, those two can always airdodge, spotdodge, or shield.
It takes some time to get used to Din's. Perhaps you haven't had the chance to try, but I'm sure you'll be able to air dodge it correctly.
Yes Pit can be hit from behind so just be wary of Zelda's hand movements and act accordingly.
This video has some examples of Din's Fire being cancelled:
http://www.youtube.com/watch?v=Rru95YGK8yg
See well Din's Fire is being handled?