eamon
Explorer
Draconic Arrogance applies to the push, not to the attack: there's no question of it "stacking" with itself on some attack.I think that it would be one push because it was one attack, so Draconic Arrogance applies once and it should not stack with itself on the same attack.
If there are two pushes, Draconic arrogance fires twice. The fact that it's one attack is just a distraction; the question whether its legal to have both of the triggers fire simultaneously - and there no rule saying otherwise, so that's cautiously yes; although it's an odd combination.
Suppose you had a weapon that pushes on a crit, and you crit with tide of iron: can you push twice - once due to the Hit: line of Tide of Iron, and once due to the crit-effect of the weapon?
In general, if something doesn't stack, that's explicitly mentioned. Vulnerabilities, temporary hitpoints; these things don't stack. There's no such restriction for Damage or Movement in general nor forced movement in particular.
It's just a slightly odd corner case - particularly since suddenly pushing someone 10 squares could count as anywhere between 1 and 10 "pushes", a concept that doesn't seem to make much sense in-game. It's not like damage, where one can make the argument that 20 damage represents a single intensive blow and twice 10 two distinct slightly weaker sources; after all, movement is resolved sequentially (so you can't take both triggers simultaneously). And does a push of 0 squares count as a push for draconic arrogance?
Basically, the concept of "a push" is not something other rules should ideally trigger on at all. To the extent that they do, however, this looks like a pretty minor issue.